You know, all these charges of "anime" stylings are really, really starting to get on my nerves.
I don't know what art you're looking at (or, alternatively, which anime you've seen), but I can see no conceivable way any parallel could be drawn between 3rd edition's style and anime.
Don't get me wrong, I love anime, but I just don't see any resemblance.
First of all, anime is primarily an animation style and so the bulk of it is simple line artwork and simple coloring/shading. 3rd edition's art is almost exclusively full blown paintings.
Anime has a very, very distinctive look to it, typified by long limbs, large eyes, crazy hair styles. I've heard people complaining about the body proportions of 3e art, but not being an artist or physician myself I just don't see it. In addition, 3e art definitely doesn't have the large eyes or crazy hair.
I guess the only real parallel I can see is that action in anime tends to be very over the top, and that does seem to be what 3e is going for as well... But I think that owes more to an attempt at emulating pulpy action. Anyways, even here, the parallel's not very strong.