Nicely said about the FAA license being an ICAO license but there is one teeny twist in there. The U.S. is an ICAO member and e.g. Austria is an ICAO member.
Please explain then if one comes rattling on the door with a FAA certificate this individual has to do the whole lot of ground examinations to obtain an austrian pilot certificate - knowingly Austria is not JAA but ICAO at least until now.