As this question was proposed as hypothetical & not a current situation, a couple of points should be noted.
1. The AMM/MPD/MRB will usually (but not always) establish the hierarchal order of documents. This is usually found up the front before you get to the bit that tells you how to do what you do. It can take some finding.
2. Often (but again not always) an approved maintenance system will also spell this out if it is not in the OEM books, including the system of maintenances status in this structure.
3. If you are operating to a system of maintenance & the system of maintenance states that you will comply with mandatory service bulletins, then under your own system an AD is not required to make it mandatory. IE the regulator does not need to get involved to require compliance.
It is not inknown for an operator to be penalised for not performing mandatory SB's without an AD in such circumstance.
Check your system you may find the answer there.
TT