Science

Sorry beforehand for the wall of text.

I would still disagree with the statement that AAE could be considered equally proper to textbook, grammatically correct according to the Oxford English dictionary (or the American equivalent).

The reason why AAE is considered less acceptable than SAE (Standard American English) is not "within" the AAE varieties. It's solely social factors - people point to "he is working" and say "this is right", then they point at "he working" and say "this is wrong".

Dictionaries are only part of that. We (people in general) assign authoritativeness to them to dictate what's the standard is supposed to be, but that authority is not intrinsic either. For example if people mass decided to ditch the Oxford English dictionary, suddenly it stops being a reference to what's "correct" vs. "wrong" English.

A dialect by definition is an adaptation of the language from the standard ‘proper’ grammatical rules.

Emphasis mine. That's incorrect.

There are multiple definitions of dialect. Plenty focus on mutual intelligibility - if speakers of two varieties can communicate just fine, their varieties are a dialect of the same language, independently of what you consider standard.

The nearest of what you're saying would be the ones referring to the standard as an asbau variety, with the dialects being the varieties "roofed" by that standard, but not undergoing the same process by themselves.

However, not even in the later the dialect needs to be "an adaptation" of the standard. Sometimes both originated independently from the same source, like French (standard) and Norman (dialect), both from Late Latin; sometimes the standard itself is an "adaptation" of a dialect, like Standard Italian (basically a spin-off of the Tuscan dialect). And sometimes the standard was formed from multiple dialects, like Standard German did.

Focusing on AAE, it's disputed where it comes from, but it's certainly not from SAE. Some claim that it's a divergent form of Dixie English, some claim that it's a decreolised creole, but in neither case the origin is SAE, they simply developed side-to-side.