Jeezy never claimed that he was in the streets WITH BMF.
He's never claimed any specifics about any of his dealings, he's not trying to dry snitch on himself. The word has always been that he (or more specifically very close friends of his) did business with other friends of his that were "members" of BMF. But his friendship with Meech was based on entertainment which turned into a friendship. And I don't know what type of dude you think Jeezy says he is, but if you listen to his music he's not trying to paint himself as some type of international drug lord.
He talks about having 2-300k, a leased sports car, a chevy and a few chains. He talks about working 12 hours a day in the projects packing O's and on, flipping packs in small towns etc, not being on boats and shyt.