These are two separate deals;
On one hand, the above quoted part of the CFR says that you military physical "counts" for certain types of flying.
On the other hand, there are also some Flight Surgeons who are qualified to issue FAA 2nd Class medicals as a separate but parallel process to your annual flight physical. Not all Flight Docs are authorized to do this, and you'll have to specifically ask them to do the additional paperwork with your PHA to get the FAA medical issued.