Why would they need to create such a sophisticated system, if all real money creation (at least in the US) is controlled and governed by them?
Also, they might not like the idea of privacy coin, ringCT, and future projects that will enable truly private transactions. So why would they create it?
I think it could be a nice instrument to catch the criminals by the way.
In general, I feel like the whole theory that the FBI or any other security agency is behind the creation of bitcoin is pretty far fetched. If it was an instrument to catch criminals, then it would make sense that it wouldn't be anonymous. The anonymity is one of the most important parts of bitcoin, so the fact that it's implemented makes it pretty hard to see as an FBI product unless there's some backdoor that magically hasn't been found yet.
It's possible that a different crypto is a part of an FBI creation, but I don't think bitcoin is one of those coins.