That’s why when you take Spanish, or German, or French in school, you learn the “Old Country” dialect. Kind of like when you hear a person from a former British colony speak, they speak with a “King’s english” accent, even thought they are of say Malay descent. The Brits kind of laugh at “American” english. They think we are rubes. Just like the French think Canadian “french” is inferior. Like you said, probably the same with real Spanish and “Mexican”.
Well, I laugh at a few of my Brit in-laws, because some of them do not speak very clearly. Though in general, my Brit in-laws speak better English than we do. The "Received Pronunciation" or Tony Blair-type English is actually spoken by very few English. Most have an accent related to the area where they grew up. And every large English city or area has a different accent. Somebody speaking with the RP or "posh accent" is looked at as someone trying to put on airs. My wife comes from the Norwich area, and she still uses a few words that would not be called proper English. Of which I never forget to remind her. Naturally, she never fails to snicker at some of my Wisconsinisms.