Westeros: A Game of Thrones.

[Kagemusha]

Oh you mean that. I would think no matter if Joffrey killed the Leader of their house and Warden of The North unlawfully or lawfully. There is little chance they would like to negotiate with him in situation where Joffrey is not the only claimant to the throne. You just dont kill leaders of mighty families wihout consequences.

Edit: Reading your edit does not chance my attitude. The Sympathies of house Stark and their vassals are definitely not with King Joffrey after killing Ned Stark.No matter what kind of explanations are given out in order to explain the act.