The separation of powers angle he's talking about does not seem to have much merit. Is he getting paid by the federal government? Does he have authority within the government? Was he hired by Bush? Yes to those answers clinches it for me. That puts him as part of the exective branch, and that branch is constitutionally accountable to the House for how it spends money.
It seems that he's trying to pull off a Hillary-healthcare-like "I'm not really in a government post, so you can't touch me" kind of thing.