for reasons I don't pretend to understand, you can fly a G-reg aircraft under VFR on an FAA licence, anywhere that the G-reg can go. 2D may be able to explain the various bits of law that make it so, but I am firmly convinced it is so.
If you have an FAA licence issued on the back of your CAA/JAA licence, you still need a BFR for the FAA bit - as well as for the JAA bit. Them's the rules. I know it may mean two BFRs in a week - one for the JAA, one for the FAA - but there you go.