When I flew B747F on a Singapore licence I flew with an EU F/O who had a FAA PPL in addition to his CAAS ATPL. On a layover at ANC he called in at the local FAA office to check his FAA PPL was still good to hire a light aircraft with in USA. They checked his FAA licence, CAAS licence and EU licence and his log books (he had just joined us from a EU loco) and gave him (for free) a B737 rating on his FAA PPL. Obviously he couldn't fly it for revenue purposes but in theory he could private hire a B737 in USA for recreational flying if he so wished.