That means that the state of registry has not only the right to licence the pilots, but the obligation to ensure the crew has one of its licences or one validated by it.
If the crew wishes to exercise its rights under Article 5 to perform international air navigation, yes. But if the state in whose airspace the aircraft is flying says "regardless of the state of registration's rules, we permit you to fly any aircraft with a licence of the following type" then the crew's compliance with Article 32 is irrelevant, as is the concept of "international air navigation".
And even if there is the the theoretical possiblity that, say, Turkey has something in their air law allowing you to fly a Kasakhstan registered aircraft on an Algerian licence, I would really like to see that regulation...
you need just one example to prove me wrong.
There's an example much closer to home. UK law permits the holder of a JAA PPL issued in any JAA state to fly a foreign-registered aircraft for private purposes (ANO Art 26(3)). The FARs render valid only licences
issued by the local authority.
"However, when the aircraft is operated within a foreign country, a current pilot license issued by the country in which the aircraft is operated may be used" (14CFR 61.3(a)(1)).
Thus the laws are potentially in conflict when it comes to the use of a non-UK-issued JAA PPL to fly an N-reg in the UK. If I'm a UK citizen (er, sorry, subject) with no intention of getting an FAA licence, why should I care if my use of an aeroplane that happens to have an 'N' painted on the side in compliance with UK law happens to violate the law of a foreign state?