You are correct in stating that the broker/dealer that BGMO bought (well, not really bought I just don't know how to describe the situation) would have to be FINRA and SEC registered. I don't think this transaction involved a private placement though. What is important is that FINRA takes six months to approve changes of ownership and they are VERY thorough. If the purchase is done through a holding company or a subsidiary, FINRA investigates every single aspect of the acquiring company including the parent company, it officers, directors and key personnel.
The source of the financing for the purchase is scrutinized as well as the personal finances of the officers, directors and key personnel. There is no way this deal (if it ever really existed) makes it past the first level of scrutiny with FINRA, not with HH's trail of unsatisfied judgments, unchallenged accusations of forgery and being an all around liar.