I have been very interested in that subject for some time now. It is true that information sharing within NATO is a reflection of what goes on between the states.
A country will choose to share certain information with one country, but not with another, even though it is an ally. There are also little clubs within NATO in all fields, including intelligence sharing, because intelligence is a very rare commodity. It is also the product of know-how. Very often, by revealing information, you may simultaneously reveal the know-how.
So there are national habits that very often re-emerge within coalitions. It is an extremely difficult thing to combat. It requires time and genuine trust between the individuals in the structures, not at the political level. It is really within the structures. It is a little like an exchange: I give you this, you lend me that. I know that's often done at a tactical level, without telling leaders. It is still a problem as old as intelligence.