Spot on. My grandparent's generation used the word "Negro", My parent's generation used the word "Colored", my generation used the word "Black", and now my daughter's generation uses the term "African-American"The problem with the hyphenated term is that it is not accurate. If someone is black, but moved here from Jamaica, are they still "African-American"? Sure, their ancestors were Africans, but that was a long time ago.
I could be a hypenated-American too, but because of my "mixed" background it would be a mouthful. How far back should I go to find my ethnicity? If "my people" originally migrated to Europe from Asia, does that make me "Asian-American"? Regardless, I don't care to be called anything but "American", thank you very much.
Taken literally, you are correct, the term African-American does appear to imply citizenship which definitely has a potential to be erroneous.
I think the main point I'm trying to make is that we as civilized people will use the terms that we are taught is respectful.
The problem with the evolution of PC is that it puts decent people on the defensive for using a terminology that was done with the intention of being respectful.