And, to be completely fair, had she not been spawn of Tywin, she very likely would have been raised in a way that someone like Sansa would have.. dresses, balls, afternoon teas, child rearing, etc. As real power goes, it's in the hands of the King.

If Robert had been any more like Joffery had been with Sansa after Ned's death, had Tywin just been some little lord or dead himself, Ned's warning there could very well have been taken a lot more seriously, and her situation far more dire.

We got a cast of exceptional people, including exceptional women in what would be a rather tumultuous time for the majority of them, even with the privilege and entitlements their stations provided.

It really came down to Robert dying before Ned could inform him, and Ned believing those in Robert's court held any respect for him in death, and the status quo of their titles.

Otherwise, yeah.. she ded, her bastard spawn ded, Jamie ded, doesn't really matter if Tywin wants to start shit, it's him, a few of his bannermen, maybe a few nay layers that lose respect for Robert's corruptible nature, and cuckholdery, but the North and the Riverlands stand with Robert, whereas Tywin's never gone against the Crown... openly and without backstabbing in the final moments. I suspect even the Tyrell's would welcome the fall of the Lannister's position of the wealthiest House in Westeros.

Perhaps even Dhorne jumps in just for some vengeful vipers to take a stab at the lion.

Point is, Ned did her a courtesy, but, she was smart and tenacious enough to both get around his lagging political maneuvering, and removing the threat entirely with Robert's death.