Liberty own FOG and employ Domenicalli, so they are the same thing, really.
I don't think Liberty are the issue, although I'm not keen on their push for more American-ising of the sport.
The FIA and their current management are the issues. Inconsist and bizarre application of rules. Ben Sulayem runs it like a totalitarian state (I thought Max Moseley was bad!)
There is no fixing that as the FIA are motorsports governing body. No one controls them.