In theory you are quite right however you can't convert a licence you haven't got. I believe it takes about 3 months for the FAA certificate to be issued! A temporary certificate airman is not valid for conversion! If the CAA refuse to issue on the basis of a test conducted before the licence is issued, then you have wasted a lot of money. In any event you can fly in the UK on the FAA licence so why bother to try and convert it in the USA?