Denmark promised to allow a fair independence vote. They certainly didn't promise to respect the results of an unfair independence vote with significant outside interference.
I'm not saying Greenland would vote to join the US! But if they do, it would be extremely hard to view Denmark as the "good guys" for rejecting it. That's a real white-man's-burden perspective.
If that was the criterion for legitimacy in such a claim for land then I have to ask, who asked the native Americans anything? Or Mexicans?
This kind of "works for me but not for you" argument, similar to the one you threw above (US to "buy democracy" by paying people to vote for independence) and then dodged any follow-up, can only take you so far in a quality conversation.