Yeah, that's 100% him paying his own hush money. Your lawyer is often an extension of you in that respect - that's why a "power of attorney" document is called that. As long as it flows through agents with that kind of close arrangement, the path the money takes doesn't matter - it's coming straight from the client. For example, my patent lawyer pays for my fees at the PTAB and then puts them on my monthly bill, but puts my name (or my corporation's) down on the form as the person who paid the fee.

Another commenter suggested that the real crime was that the expense was named incorrectly on the campaign's books, which makes more sense to me but also seems kind of tenuous.