As has been pointed out - the issue isn't Fidelity... it's the FA that is using Fidelity. Fidelity doesn't charge fees on RMD distributions.... I suspect the FA does.
I agree with the other posters that you need clarity about the trusts... are these estate planning type living trusts? Or are your parents invested in trust investments? If it's the former, they should be transferable as long as the title is maintained correctly.
Talk to your parents about moving from their current FA to a Fidelity in-house managed portfolio... Much lower fees. Since Fidelity is already the custodian, I would imagine that the transfer would be fairly straightforward. The only issue might be the push back that the FA will give... (s)he'll try to convince your parents it's a bad move to leave him/her.