I think your caution is a good way to go. Company required deadheading is not flight time, but certainly is duty and not rest (we agree on this). The regs and the FAA is very clear about that.
I will quote one more part of the reg and then let it go because we've certainly beat this to death (I hope
):
121.471(b) "...no certificate holder conducting domestic operations may schedule a
flight crewmember and no
flight crewmember may accept an assignment for
flight time during the 24 consecutive hours
preceding the scheduled completion of a flight segment without a scheduled rest..."
121.471 does not mention anywhere "duty day" and mentions the word "duty" only in the construct of 121.471(f) to make sure that airlines wouldn't try to use the deadhead home at the end of a pairing as rest before scheduling more flight time (and to make sure the airline understands deadheading is duty).