Via Author I wound up reading Jonathan Tappan's Is RWBY Anime?. Both Author and Tappan come down firmly on the side of 'no'. For myself, I don't know what to feel about the whole issue so I'm going to ramble on with some of my thoughts. I'm going to focus on manga, not because I know more about manga but because I know more about American and Western comics than I do about modern American animation.

On the one hand labels like 'American anime' and 'OEL manga' simply feel cringe-inducing to me (Tappan's description of 'sad' is an apt summary). On the other hand I feel, contra to Tappan, that Japanese anime and manga have clear stylistic differences in both writing and art from their American and Western counterparts. American comics cover a lot of ground (from big-two superhero comics out through various sorts of independent and alternate comics, including webcomics) but nowhere in this range do they really look like manga from what I've seen. I rather expect you could show people anonymized pages or panels from both American comics and Japanese manga and have them reliably pick out which is which (and do similar things with plot summaries).

(Frankly, part of this is that the average manga artist is probably better than the average American comic artist, not because of intrinsic talent but because Japan has evolved a ferociously competitive and sophisticated manga market. My impression is that you must be on the top of your game to have a chance in Japanese manga; this is not really true in America, most especially in American superhero comics.)

Given this stylistic difference and an increasing number of people in the West who've grown up reading manga, some number of them will want to create works in the style of that manga. If nothing else those are the stories and art that appeal to these creators (and some of them may have little or no exposure to American comics; just look at the relative sales figures for translated manga and traditional comics). Today we lack a good term for such works. They are not 'manga' in the sense that they are not from Japan and the Japanese manga system but at the same time they are going to be stylistically different from 'American comics'. If these new works are executed well they will be far closer in style to Japanese manga than anything else.

(One of the problems with 'OEL manga' today is that many of the works have not been executed well by Japanese standards; they would not pass muster as real manga and cannot compete with it.)

I see a similar issue happening with RWBY and animation in general. The creators of RWBY are clearly familiar with anime and are drawing much of their stylistic inspirations from it. The result today is somewhat clumsy and awkward and not entirely successful (much as OEL manga has been, although I think RWBY is better executed) but I wouldn't be surprised if that gets better as everyone involved gets more experience. And as with 'manga-style comics', we currently lack a good term for such animation and I suspect we're only going to see more of it.

(If you want to make 'grown up' animation in the west I don't think you have very many models to follow and the dominant one is likely to be anime.)

I don't think Tappan's call for animators to develop a style that's different from anime and manga is really the right approach. At its core what it amounts to is telling people not to work in the style that they like and admire simply because they are not from Japan. It's especially unlikely to work if you believe that the manga and anime style is further evolved and more artistically sophisticated and successful than the western counterparts.

(I do tend to think that anime and manga have better developed styles of art, composition, directing, and storytelling, not because of any innate superiority but simply because both fields have a lot more practice under ruthlessly competitive conditions than their Western equivalents. This commercial competition doesn't always work out artistically (see the parade of cookie-cutter anime that gets churned out every year), but it often nurtures a significant degree of competence.)

Update: see WesternAnimeFuture for more discussion of this, prompted by Author.

Update (October 16th): See also The authenticity of non-Japanese manga, by Sixten for interesting commentary.

Sidebar: the audience reason for 'OEL manga' and 'American anime'

This is obvious but worth mentioning: one pragmatic reason to stick those labels on your works today is to attract people who like manga and/or anime but do not like Western comics or Western animation. You are basically hanging out a genre sign, much like covers on fiction books.

I suspect that this is a not insignificant issue for RWBY, although it also gets to draw on a growing machinima movement in the west that is breaking out of the general confines of traditional animation.