This is part of the reason I've retroactively stopped really liking Ned. He was a, judgemental, uptight, dick. No questions asked, immediate judgement being made by him.
Yep. I still love Ned, but this is an intentional flaw of his character that keeps him necessarily believable and human just like everybody else. Ned was very honourable and caring, and his moral compass is generally pointed towards compassion and avoiding the unnecessary. Despite being Robert's close friend he was disgusted by Robert's order, during the rebellion, to have every Targarian (sp?) child hunted and killed. He didn't see the reason behind such mindless, abhorrent slaughter in a war they were winning/had won, and this is echoed later on when he refuses to support Robert on Dany's assassination. He also loathes speaking of his relationship with whoever-she-was that resulted in Snow, due to the out-of-character behaviour it was for him and how much it hurt his wife. Yet he still loves John and considers him one of his own, as noted by their parting in season one. Ned is a really good family man.
But his allegiance to honour and tradition is so far up his own arse he struggles to see outside the box. He is, in reality, actually pretty stupid when it comes to politics, if just due to inexperience. He was never supposed to rule Winterfell after all. His behaviour when confronted with difficult situations is reactionary, resorting to learned behaviour, culture, and honour often devoid of critical thinking. Almost all of his fuck-ups after Robert died were simply due to his insistence to honour Robert and what he considered rightful law, that being the throne was to go to Stannis. Similar for judging Jamie. Emotions would have been high, but Ned just doesn't have the capacity to sit down and think about how complex and grey these situations often are.
EDIT: This is not to say Jamie is a "good guy" by comparison, though. Jamie is complex. Like most things in Game of Thrones you have to look at perspectives. When Jamie attacked Ned he did so because his younger brother, who he clearly cares about, had been taken prisoner by a family that might as well be considered their enemy. And he'd been taken prisoner under false claims. We hate the Lannisters for holding Sansa hostage, but from Jamie's perspective that was what Ned and co were doing with Tyrion. His relationship with Cersei is gross, and the ramifications (bastards on the throne) serious, but his love his genuine. So...what can you say in that situation? "Don't love your sister like that". Sure, but he does, their relationship filled with more love, compassion, and sensuality that Cersei ever had with her own husband. Gross and weird as it might be for the viewer, Jamie has (or had) no less reason to commit himself to Cersei than Ned to Cat. On the other hand such commitment to love had him push a young, innocent boy out of a window and cave in his cousin's skull to escape a prison. Both of which...kinda understandable in an abstract sense from his own perspective, but still very morally questionable.
TLDR: Jamie isn't half the villain people like to make him out as. Same as Theon. Folk are just overly conditioned to two dimensional story telling elsewhere.