Yes, as far as I'm aware, the crew must hold the requisite qualifications from the country where the aircraft is registered. As I understand it, issues such as short-term leasing creates a problem and usually ends up that the leased aircraft is flown by crews who are specially imported for the term of the lease. In long term leasing, the aircraft is placed on the local register so that locally qualified crews can fly it.
There may be some differences to this in JAR-land though.