There's nothing to say that the PC's can't have disfunctional relationships with NPC relatives. We're just talking about the relationships between the PC's. You're making the "cooperative" position broader than intended. It's straw man argument.
It wasn't intended as such. But you bring up something that leads to a good solution: really in Amber, we're talking about family, so the way to create co-operation and make it look sincere is to have all the PCs be a single group within the family that are united by something that sets them apart from almost everyone else.
The "Redheads" are the classic example in Amber. They're different than the other kids, they're wierd, they're mostly nerdy (except Bleys), they've got too much magic for the average Amberite to trust them. So of course, the three of them banded together like peas in a pod, at least until Brand betrayed the other two.
So if you want your PCs to be tight, you have to do something to make them so, to explain why they would be when everyone else is double-crossing each other constantly: something that makes them different from everyone else, and makes most of the rest of the family not like or trust them.
RPGpundit