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.