There's actually a somewhat lengthy history of prominent fake Indians. In the 1930s there was Grey Owl in Canada, who it turns out was actually an Englishman born and raised in England. Then there was Iron Eyes Cody, who was actually of entirely Italian origin.
I'm not sure if it is motivated by the seeds of self-loathing planted in people of Western origin, or the pseudo-religion of communing with nature and how the American Indian must be the template of perfect harmony with nature (i.e. just a modern rehash of the old Noble Savage mythology).
It's also in a way indicative of the white liberals' own peculiar brand of racism that makes a big deal out of not being racist....because you just know people like Churchill feel imbued with some sense of magnanimity, as if to say "Fear not! For I have deigned to take up your cause as I ride to the rescue on my white horse." As if to say you can put your minds at ease, because an enlightened white liberal has seen fit to take notice of your cause.