This all makes sense and I'm sure that they do offer lower offers to those from disadvantaged backgrounds.
The reason for my belief of them offering AAB offers if they exceptionally like one bit of an application is because me and one other person in my class were offered AAB offers. I do not have the best grades (although still good) with 7A* 4A at GCSE and AAA predicted. The other person, however, has straight A*s in everything. We both talked and we do not fit any of the criteria- we go to a good school (where academic achievement is quite high) and are from decent areas.
The other 2 people in my school who also applied Notts law (one with straight A* and one with similar grades to me) got AAA offers however. Unless it was a mistake, the only thing I can think of is as they liked the rest of application, excluding grades, so they offered us lower offers.
Regarding the OP, if AAB offers are being made, not just for contextual reasons, then it seems to me that if the other aspects of his application were good/excellent, he/she stands a chance.