Talk to 3 different FSDOs and get three different answers. It is amazing how different they interpret rules. I actually had to go to a different state to get my military flying converted to a CPL because the FSDOs in one state claimed I couldn't do it and another said I could.
I got the same answer as you when I contacted a FSDO in Dallas, but later found the correct answer myself.
And yes, Johnny 7, you did give me a couple of permanent grey hairs.