In what way? The territories are as much a part of the US as the states are. They simply have a different status than the states do.
I assume you're making some point/remark regarding their status and the political mindfield surrounding it, but that doesn't change their subnational/sovereign situation.
I'm well aware of it's political decisiveness in LATAM, but it's pretty clear the context here is the colloquial usage in English; despite your personal feelings.
Well, US people are prompt to point finger at the rest of the world and tell them how they should treat/call other peoples in order to not hurt them, so I think it is valid from non US people to tell US people to also fix their colloquial usage if it is rude towards other nations. Also colloquial doesn't mean universal.
You know, putting your own house in order and stuff like that.
The colloquial usage is far greater than the US. Go watch some German, Dutch, British, Australian, French, etc media and then come back and talk.
Your umbrage at the word is your problem and your insecurity. Americans are quite aware of the difference between America and America, and it's pretty clear in context. As a Spanish speaker, it's also obvious in 99% of contexts in Spanish. So there's nothing to fix beyond your feelings, which affects no one but yourself.
There's nothing to "play" here. Taking a misguided emotional stance on something that has very little effect on anyone and misattributing it to a "big bad" is a clear sign of personal insecurity.
If you're not Latino, it's even further mind-boggling how you would think this was an American derived phenomenon or in any way unique to American language. It goes back to intra-European communique well before the revolution and any concept of the US began.
Lastly: I'm Mexican, living in Mexico. Literally the only time I've ever heard any Latino refer to themselves as "American" (in English or Spanish) is specifically for the made up injustice you seem to have latched onto. So again, there's nothing to fix, beyond your hurt feelings and insecurities (vicarious or internalized), since the language is unambiguous.
I'm sure you'll have something to argue back with or some weird little nitpick that makes you think you've "won" though...so you can have the last word. Ciao.