Mizuo's magic is not just her beauty, but the grace she brings to the role of America's second most famous Native American woman (only Pocahantas has received more attention through the centuries). Many Native Americans were disappointed to learn that this role was given to someone of different ethnic heritage, but then no one in the Italian community complained that the role of Octavius (Augustus Caesar) was given to a British actor (Steve Coogan). In the end, the movie is what it is.
In other words, this writer's argument is pretty weak. Here's a Native writer's rebuttal:
Tara Beagan presents a Native American Perspective
This would have been an unacceptable stereotype in any of the other existing cultures represented in the film. Suppose Ben Stiller had embodied the stereotypes that so many lazy, uninformed people assign to Jews? I will allow you to imagine how that might have gone down, and how ugly and inappropriate that would clearly be.
Beagan could've made her argument even better. Consider all the historical figures in the Night in the Museum franchise. Were any of the white figures played by people of other races? I don't know, but I'm guessing not.
If not, why not? Why not have a black woman play Amelia Earhart or a Chinese man play Teddy Roosevelt? Heck, why not get Denzel Washington to play Earhart and Lucy Liu to play Roosevelt? Do you want the best actors possible or actors who are "politically correct"--i.e., race- and gender-appropriate?
Would anybody object to these choices? Of course they would. White people are played by white people because they're the norm. You don't tamper with something that "everyone knows" is right.
Only exotic "others" (e.g., an Egyptian or Sacagawea) get cast as if their race doesn't matter. To most Americans, a Japanese woman is as "foreign" as a Native woman. Because they're not (white) like us, the details don't matter. One brown-skin is as good as another.
Night at the Museum embodies an attitude we see whenever non-Natives are cast as Natives. We might call it the "They all look the same to me" attitude. Needless to say, it's racist.
For more on the subject, see Friday, Tonto, Jacob Black, et al. and The Best Indian Movies.