They don't really bring it up much on the show, but Catelyn is also revered because of her father, Hoster Tully. Many of the men who swore themselves to Robb did so because of the Tully connection - Robb's great uncle Brynden Tully is also aiding him. It's also why Robb was able to cross the bridge at the Trident - the Freys were one of the houses pledged to House Tully. Walder Frey (the one in charge - from the books we know that you can't swing a dead cat without hitting someone named Walder! Even Hodor's name is actually Walder.) would have been even less willing to speak with Catelyn, in spite of the little slights he threw in her face, if not for the Tully connection.
Just to add a bit more from the book....the man who wanted to kill Jaime when he was recaptured - the one whose son Jaime killed when he escaped - is Lord Rickard Karstark. He good reason to want Jaime dead. Jaime killed two of his sons in book 1 in action we didn't see on the show - this was the battle stuff they didn't have the budget to film. Karstark was already gunning for Jaime before Jaime killed another one of his sons.
I don't think Robb is nearly the man that Ned was. Yes, Ned had a ridiculously rigid sense of right and wrong that eventually got him killed, but he was also much smarter than Robb. I think JON is Ned's true son. Bran is smarter than Robb as well, IMO. Again, I may just feel this way because Robb isn't a POV character in the books, while Jon and Bran are.