So far, we've been talking about anime in D&D in pretty general terms. But, the problem is when you start looking at specific instances, the anime comparisons fall all to pieces with even the most cursory of investigation.
Take the whole "3e art looks like anime" bit. It's now moving into 4e already. Yet, despite repeated calls, not one single person has been able to produce a single WOTC pic in a D&D book that looks remotely "anime". Not once. Ever. I've seen thread after thread whinging about 3e art and comparing it to anime, but, whenever someone asks for concrete examples, everyone shuffles their feet and hems and haws.
For another example, look at the Pokemount. Comparing the paladin's mount to Pokemon to show how bad the mechanics are. It doesn't really work though since a paladin's mount and a Pokemon share no real points of comparison other than they can both be summoned. A Pokemon is a small magical animal that pops out to fight with magical energy attacks on behalf of its summoner. A paladin's mount is a large creature that rarely fights and is mostly only there as background fluff.
A better comparison is a Baq of Tricks. That's pretty much Pokemon to a "T". Only problem is, it predates Pokemon by a couple of decades. Pretty hard to say that it's inspired by anime.

A druid's summoning ability is far closer to Pokemon than a Paladin's mount, yet, we rarely see thread after thread whining about how the Pokedruid is ruining the game. Of course, it's pretty hard to ignore the fact that a nature based character summoning nature spirits to defend the land is pretty solidly entrenched in Western fantasy as well. Sure, a Druid's summoning can be compared to Pokemon, but, it can also be equally compared to a host of myth and fantasy as well.
When you boil it down, anime comparisons are simply an alpha geek's way of trying to tell people that his fantasy is better than yours.