The American English language is a hodgepodge of various romantic languages. What makes a word 'english' (at least according to many dictionaries) is common acceptance and use.
In general, the use of the word "ain't" was considered as slang.
It is, whether we like it or not, a part of 'our' language.
What helps me to understand, is that with 'ghetto-speak', most 'english' rules are thrown out the window, so usage of the word "ain't" is likely a habit of clture for Michelle, and not an indicator of her 'ability'.
“It is, whether we like it or not, a part of ‘our’ language.”
This is my attitude. The grammarians can rail against it all they want, but the word has a long provenance and is commonly used, so it is just as much a valid English word as any other. I wouldn’t use it in a formal setting, but it’s quite silly to try to stamp out a word that is so commonplace.