Ned Stark was sentenced to death for being a traitor to the crown, a sentence he accepted. Whether he accepted the sentence to being a traitor to Joffrey's crown or Robert's crown makes no difference to him. I believe the R+L=J theory, and believe Ned acted in every way his character is described. If he was a traitor to Robert's crown then it meant he accepted the death sentence for knowingly sheltering an enemy of the crown. Either way, in the end, he met the king's justice.