A TRE with an IAA licence can't legally sign a type, or instrument rating, on a UK ATPL. He can on a JAA ATPL.
So, although you can legally fly RYR aircraft on a UK licence, in order to keep your licence current, you will need a UK licence holder to sign the validation, therefore RYR prefer a JAA licence.
This is direct from those awfully nice CAA licencing people.
(see CAA licencing rip off? post in the Questions forum).