I have always pondered this question so I quickly went to the link and was confronted with a really weak and half-baked argument. First, this is not a question of American audiences; I'm not American and love anime but they don't look Japanese to me either.
"The Other has to be marked. If there are no stereotyped markings of otherness, then white is assumed." This may be true but it has very little to do with anime. As others have pointed out (i) anime artists have been influenced by their Western counterparts (anime is not a traditional Japanese art form, you know) and (ii) commercial considerations play a role, i.e. very Japanese looking characters would have less appeal to a large audience.
But forget about that and just think about the argument to see how faulty it is: In its essence it is trying to show how lop-sided white Westerners see the world but it itself is also very prejudiced. Do you think when a Chinese person looks at an anime character they think it's Chinese (because "otherness" isn't marked)? This sort of thinking is typical of a lot of mumbo-jumbo that comes out of English departments under literary criticism. If Japanese didn't have to mark "otherness", why are the characters in traditional Japanese paintings look very Japanese (slanted eyes, hairdo, etc.).
In the end the article states: "Some Americans, even some scholars, will argue against this view of anime. They want to think the Japanese worship America or worship whiteness and use anime to prove it. But they seem to be driven more by their own racism and nationalism than anything else." This is another common tactic: when someone raises a problematic viewpoint, label them as racist, misogynistic, or worse (e.g. see the Summers episode).
How can you explain that a lot of Japanese women go through cosmetic surgery to get rid of the slant in their eyes to make them look more Western? Why is baseball so popular in Japan? Japan has had a long love/hate relationship with the US (and Westerners in general). I'm not saying some form of American idealization is at the heart of anime styles but I think it has definitely influenced it.
EDIT: For similar over the top ideas about race and culture and to see how politicized the debate can be, see http://en.wikipedia.org/wiki/Ancient_Egyptian_race_controver...