As I indicated, the above is my interpretation. Implicit in that statement is that I may be wrong.
However, it is certainly true that JAR licences were not acceptable to the US authorities for flying N registered machimes outside the licence holder's state of issue. Here is an extract of an exchange between the FAA and an individual enquiring about the validity of a Belgian-issued JAR licence for the purposse of flying a N registered aircraft outside the US:
The question presented is whether under 14 CFR §61.3(a), the pilot is permitted to operate a U.S.-registered aircraft in any foreign country in which his Belgian/JAA pilot license is recognized. As explained below, the Federal regulations under Title 14 of the Code of Federal Regulations (14 CFR) and the U.S. obligations under Article 1 of the 1944 Convention on International Civil Aviation (the Chicago Convention)' do not permit such action.
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.
I have, as yet, been unable to uncover a similar ruling or opinion concerning licences issued in accordance with Part-FCL but can think of no reason why the FAA's view should be any different.