The behavior problem with American Pitbull Terriers is far more than an issue with poor training, though certainly that is part of it. Primarily its a history of several generations of animal husbandry in the US with the specific intent to breed a more vicious dog. All Bull Terrier breeds do have aggressive tendencies and for several decades now unethical breeds over here have selectively bred them to be extremely vicious.
It's definitely true that you see the vicious line of APT's amongst the poor since those are the ones who've bred them to fight and to be the poor man's security system.