The island has been beholden to external parties and interests for centuries, seldom actually enjoying more than a modicum of self-determination. I see the autonomy granted them in 1979 (and further powers in 2009) by Denmark as being uncharacteristically benevolent for international standards, and something that would never be realised in a million years under the USA (particularly with their military presence).
I'd understand if Greenlanders never felt much kinship for the Danes, but I'd be hard-pressed to accept they'd feel any more for Americans. And I can't find any source referencing Greenland's sentiment towards this offer of acceding control to a global superpower they'd likely never enjoy independence from. Do we know if Denmark just did them a favour out of altruism here?