What you do in a countries airspace in its registred aircraft has nothing to do with any other country. Your license is only there to prove to the authority you know what your doing. If they decide your good to go under certain conditions outside your license rights thats up to them on home turf.
Its quite normal for commercial pilots to fly on validations and for us to be given rights which we don't have on our home licenses. TRE rights and TRI are the usual favorites.