In Greenland's case, specific issues regarding their own rule and such are rather huge issues for those people. They were under Danish rule prior to WW2, but after the invasion by the Germans, they came under US rule. After the war, contrary to all our assurances otherwise, they were returned to Danish rule instead of being given autonomy. It is incidental that they are self governing now as they are still considered a Danish territory.
Furthermore, the levels of economic aid that were promised post war never came. It is the same all over the Pacific. With the exception of the Phillipines, we broke all promises we made to guarantee basing rights. It is no wonder that the native people of those areas hate us. In some cases, we never even cleaned up bomb dispersal sights or we left massive amounts of hazardous waste to poison the land of these people.
Now we ***** and whine over not being able to get back something that they (the people of these places who live in squalor) consider to be nothing more than novelty items that only a rediculously rich nation like America can afford.
The Greenland issue also includes some very specific contractual issues that were not fulfilled. Specifically the return of an aircraft to the Danes. Imagine how the people of Greenland feel. It is their land and their property in that ice shelf.