I think it is a cultural thing, but thinking about it now it would sound really similar to how you describe if they were chanting "America" instead of "USA".

I don't know, but the point is that I can see where you are coming from. I think that the "USA" thing has become "normalized" to me because of other things in the media (sports, wartime, etc...) that it doesn't phase me, but changing the wording makes it pretty clear.