Gosh. This is actually a very difficult and complex question, spanning way beyond the stance tf2chan takes on 'style'. It is something I think every artist (including myself) struggles with. I briefly touched on the subject on point 5 in the original post, but I will expand further on stylization. There are three major points in this essay: What is stylizaton, unintentional vs intentional stylization, and incorrect stylization. This is also a rough draft, so bear with me. I may expand on some parts that need expanding later. As always, feel free to discuss. I also hope this answers your question, as well as educates others on 'style'.
1) First of all: what is stylization?
Stylization, to me, is a standard group of symbols, deviations, or shortcuts that an artist makes when representing reality. This can be applied to most things. Line weights, pointed noses, large heads, dull/bright colors, blocky painting, JJ Abrams' undying devotion to lensflare - are all legitimate examples of stylization. To limit length and relevance, I'm simply going to address cartooning, specifically of human figures, in this essay.
There are certain groups of stylizations (such as anime) where figures typically follow particular trends - for example, large eyes, diminished noses, exaggerated hair, and thin, somewhat uniform body types are some that come to mind when someone says "anime". There is generally less emphasis on western shilouettes and more on frills, color palettes, and interchangeable aspects like hairstyles to define one character from another.
Team Fortress 2 is the complete opposite. The art style relies very heavily on shilouettes and exaggerations bone/muscle structures to define characters - this is particularly important in game design, where you have to be able to identify what class a person is and what team they are on from across the map and respond accordingly. As mentioned in the commentary for the game, the shilouettes are designed to also draw attention to the weapon the character is holding (ex guns are always held in front of the character, melees stick out to the side, and their shape is always very clear, even from a far distance.) Color palettes have little variation from character to character, but the body types and facial aspects are so different that no one would have any trouble distinguishing one from another. When game critics mention that TF2 is groundbreaking in that it's a fps with personality, they also take a jab at games like Crysis have issues - all their main characters have nearly interchangable builds and heights.
Neither of these ways of stylization are "Correct" ones. They actually have much in common - use of symbols, exaggeration/minimization of certain aspects of the human form, and approaches to deferintiating characters. However, I believe that some anime and TF2 are clear examples of deliberate stylization - and in almost all major aspects, deliberate stylization is almost entirely superior to unintentional stylization, which brings me to my next point.
2) Deliberate Stylization vs. Unintentional stylization
This is where I agree and disagree with the chan's general stance on anime and stylization. The root of this dislike is that many new artists start learning from anime, and therefore are riddled with holes in knowledge. They start by copying anime, instead of studying from the source of anime (real life), and therefore only transposing symbols (a certain way to draw an eye, perhaps, or a generic face shape). In short, they cannot distinguish between what the symbol of the eye represents and what an eye is actually supposed to look like (please read Scott McCloud's book, Understanding Comics, or click on the second link on the previous post >>1371).
When people try to reconcile the simplistic symbols they learned from anime or any other cartooning style with the entirely different (and I would have to argue, more complex, and infinitely harder to copy via symbol-learning) mass-based art style of TF2, usually disaster occurs. This particular problem is VERY common on this board, as well as /fanart/, in certain ways. It happened for me. Faces are one of my weaker points as an artist, and I am usually able to approximate facial structures via a very complex database of symbols I use, but I struggled for a large chunk of time with tf2's particular facial structures, some of which I still haven't completely nailed down yet, and have trouble imagining the features in three-dimensional space, as I should be.
A similar thing happens when artists try to switch from anime to semi-realism. second part of her essay (link is in the comments) talks about "Patterns and Anti-patterns", and cites a common stylization anti-pattern that artists transitioning from anime to semi-realism have.
The point is (and I know I've gotten a little bit off-topic here) that all this talk of pre-learnt symbols is a clear example of unintentional stylization in newer artists. By learning symbols from pre-existing styles instead of doing foundation work (studying from life, thinking critically about the human figure) they shunt themselves into a box, so to speak, and make it difficult to learn other styles, or create new styles that are not derivative of the previous one they learned.
TF2chan, in particular, has a major beef with unintentional stylization (specifically tied to newer artists that derive from anime-specific symbols), but tf2chan users generally are not very clear about WHY they dislike it. I'm under the impression that many of them do not actually know. The 'dead horse' aspect you mentioned comes from the accepted idea that 'Style is not an excuse, don't use it if you're bad' - but this is only one very small facet of the larger question. "JUST HUDDLE TOGETHER, KEEP THE ANIME OUT."
However, there are still ways for style to be wrong, and not all of these stem from unintentional stylization.
3) When is Stylization Incorrect? What happens if a style is lacking in aesthetic value?
This is the part where things get REALLY subjective (as if they weren't enough!) Disregarding clear examples of using 'style' to cover anatomy flaws, a good old standby rule I use is: If it looks wrong, it probably is. Every critic's worst nightmare is the artist that goes "But it's supposed to be like that, I'm attempting ______ style", or something to that extent in defense of their drawing. The best way to counteract this is to try to attempt to see it from the aritst's point of view, pinpoint what looks wrong and why it looks wrong within the confines of what they specified - and hope that they can see your point of view as well.
I'm not sure who Joel is, but yes, 'cartoony' styles can be just as wrong as 'anime' ones - but the wrongdoings are more difficult to spot for newer critiquers who are not familiar with what they should be looking for. Typical problems I have with artists badly attempting a 'cartoony' style: Stiffness, flatness of the figure, symbols (again), lack of true anatomical understanding, and lack of aesthetic value.
While we're on aesthetics, I will assert that it is important to admit your subjective preferences, especially when critiquing style. I have seen a few styles where the exaggerations are very deliberately done, but I don't find particularly attractive. It's subjective to the point where I can't really criticize the artist.
Sometimes a style is straddling the divide, where it's attempting to exaggerate proportions but not quite there, and instead just makes the viewer feel that the artist is mucking up the anatomy. In this case, I like to say that "If you meant to stylize it, I think it should be stylized further, but ____ looks wrong when the rest of the anatomy is correct." I ran into a similar problem with my TF2 Girls drawing (http://tinyurl.com/3efzndc) where some of them looked a little too thin considering how the rest of the image was drawn, but I ultimately concluded that there should have been more stylization to achieve the look I was going for (which I fell short from), instead of less. Style is one of those things where someone goes "there's something wrong with this picture but I don't know what", but it is very possible to pinpoint those things, even if they may be more nebulous than expected.
So where is this line, precisely? I would have to say that it's not really anywhere, in the same way that there isn't a huge distinction between the stuff in /fanart/ or /fanfic/ and the stuff in /workshop/ besides one of them boards means you're specifically asking for crit and the other doesn't.
4) The Importance of Style
One shouldn't take away from this essay, or TF2chan, that Style Is Bad. I personally wasn't very read-up on the term myself until a short while ago, so I was afraid of the world of a long time. Style is, in fact, critically important for an artist, to define and differentiate yourself from millions of people, to show that you have something new and creative to share (or even just an impressive way of repackaging old styles!), and to explore the boundaries of art.
My stance on style isn't nearly as militant as igpd's (http://icrit.org/style.html), but I can agree with him in that studying from life will do nothing but help whatever style you aspire to. Unlike him, though, I disagree about HAVING to learn realism to a near-perfect extent before attempting ANY sort of stylization whatsoever.
Many great modern artists do not have the exceedingly solid foundations similar to Picasso that he discribes, but enjoy a very complex and concrete 'style'.
Most importantly, do not wait until you know what direction you want to go in, or what you want to be, to start arting! Just go make stuff. I find that it's the process of making things that you will discover all that stuff like what kind of style you want to have.