Those international obligations (under the Chicago Convention) mean that it must grant foreign registered aircraft the right to perform international air navigation based on flight crew licences issued or rendered valid by the state of registry.
Article 5 of the convention says (amongst other things)
Each contracting State agrees that all aircraft of the other contracting States, being aircraft not engaged in scheduled international air services shall have the right, subject to the observance of the terms of this Convention, to make flights into or in transit non-stop across its territory and to make stops for non-traffic purposes without the necessity of obtaining prior permission...
So you are right that countries have to grant overflight and landing rights as long as the other rules are adhered to.
If it chooses to make more permissive regulations than the state of registry does, it's difficult to see what jurisdiction the state of registry would have, particularly if the crew were not nationals of the state of registry.
Article 32 of the Chicago Convention says
a) The pilot of every aircraft and the other members of the operating crew of every aircraft engaged in international navigation shall be provided with certificates of competency and licenses issued or rendered valid by the State in which the aircraft is registered.
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.
So I don't think the convention helps here at all.
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.