That was my understanding as well. What made me think though was when I converted to a full FAA certificate the DPE I talked to originally said that I would need HP for my own aircraft despite being a JAA Instructor as well as differences training etc which I can already give. It all seemed a bit odd.
That's because when you fly an 'N' reg aircraft on your 61.75 foreign based certificate, you are effectively exercising the privileges of your
foreign licence, albeit that the 61.75 certificate enables you to do so on an 'N' registered aeroplane.
Once you have a stand alone FAA licence, you will then be exercising the privileges of THAT licence, so whatever JAA qualifications you may have, become irrelevant.