Well, it's not a theory. More like a thought. I believe there has to be some sort of connection between Smith (a known member of TT) asking "Exactly how much does Jane know?"  in 6.02 and the PI saying that her client wanted to know everything Jane and the team knew (6,05), That kinda implies that RJ didn't hire the PI but the "Tigers" did.

Also, as some people have stated, it's never been a problem for RJ to be aware of Jane's and Lisbon's plans.