The attitude that your comment reflects crops up a lot in relation to, for example, the Washington Redskins naming controversy. Folks who like the current name are always bringing up a couple of examples of Native Americans who say they “don’t care” about the name, and claiming that it’s really only white liberals who are offended; meanwhile, in my experience, the large majority of Natives actually do care very much, and are upset that a racial slur used for their ethnicity is being used as the name of a sports team.
I found this comment rather funny, because if CGP Grey is correct [0] the preferred term by American Indians is "American Indian", NOT "Native American". So you're claiming knowledge of the general opinion of a group, while not using the group's preferred name for themselves.
This is one of those things you can find out for yourself: go to a pow-wow (non-native visitors are typically very welcome) and ask the people there how they usually refer to themselves.