Anyway, when did it become the role of members outside a group to tell them whether or not they should be offended by the name they are called?
Um, when they started calling them names? Now, don't take this the wrong way, but that sounds a little defensive. It's quite normal for people to explain the reason they chose a particular characterization of a group, that name catching on, and the other group getting affronted at being called a group. At this point a new characterization, one without connotations, is found. All along, people keep explaining that there's nothing bad at being in a group, or alternately that grouping is only done to divide and conquer.
no one ever uses the term Americans to refer to all inhabitants of the North and South Americas.
And that'll be because they know they'd be misunderstood. I used to call people from the USA "people from the United States", but that got too cumbersome. So I switched to Yanks - fully aware that it is also a poor choice of word, but at least more specific and apolitical around here. I've most recently transitioned to "American" plus qualifiers (such as state), since I've been reading stuff written by themselves. I don't see any other words coming beyond the horizon, except maybe cultural ones.
However, I wouldn't put calling all inhabitants of the Americas "American" past biologists and other non-geopolitically minded people.