- Eddard Stark knew the worst of the Lannisters and that they couldn't be trusted
- Was aware that his predecessor was murdered for knowing this, and that the Lannisters had a hand in it
- Was aware that they attempted to murder his son for knowing this, and that the Lannisters had a hand in it
- Was aware that he had no real friends besides the King, and that he was vulnerable without the King.
- Was aware that there had been an attempt to murder the King before in a plot, trying to get him to participate in the tournament, and that the Lannisters were involved
- Catelyn pointed out that Eddard knew certain men were not to be trusted and should be mistrusted. So him lacking experience in 'court intrigue' isn't too strong. Certainly the game in the north isn't as devious as in the south, but it's not innocent either.
- Was trying to escape several times, knowing he had to move fast to stay alive
All in all, Eddard telling Cersei as an 'out' is not only extremely naive with the knowledge Eddard had, but also out of character considering that Eddard was far more careful and distrusting of Lannisters than he was in that chapter. I do not understand WHY he did as he did. Apart from that the author wanted it desperately and then wrote it even if it makes no sense.