This question was raised at an FAA meeting regarding N reg in Europe held at Luton Airport earlier this year (I was there too!). Present were several FAA representitives including an FAA lawyer and this question was raised. Their reply was FAR 61.3 is strictly enforced, and so as IO points out, the "country in which the certificate is issued" is therefore strictly enforced. The Chief Consul has issued interpretations on this and can be found on their website where someone has asked this very question with the example of a Belgium pilot flying an N reg on a Belgium JAA PPL cross borders.
To save the bother of finding it, here is an extract:
Section 61.3(a) (1) of the Federal regulations states "when [an] aircraft is operated within a foreign country, a current pilot license issued by the country in which the aircraft is operated may be used." A strict reading of the rule requires that the country of issuance of the pilot's license match the country in which the aircraft is operated. The FAA, through an interpretation, cannot extend the meaning of "country" under § 61.3 to include JAA member States. Additionally, Article 32a of The Chicago Convention requires that a pilot license match the state of registration of the aircraft, unless a validation is made. The FAA made a specific grant of validation respecting the Belgian license whereby a U.S.-registered aircraft may only be flown within Belgium by a Belgian licensed pilot. No JAA agreement can extend that specific validation.