If Ned survived, he’d be able to tell Catelyn how Littlefinger betrayed him.
This could explain why he was in King’s Landing rather than Braavos in season 1.
It seems unlikely, given that Cersei’s soldiers killed most of the people in the Starks' service.
This would explain why he’d allow himself to be imprisoned and travel with Yoren.
And he would have been more inconspicuous, arriving with so many others.
But this is something that the series would likely have mentioned eventually.
Although the Faceless Men are powerful opponents, they aren’t infallible.
And a world like George R.R.
Martin’s constantly proves that even the strongest and smartest characters can falter.
Therefore, this theory does hold some weight.
