Robb did not officially make his decree to have Jon Snow legitimized and named next in the line of succession until after he had left Riverrun and was on his way to the Twins. And once at the Twins, who knows what Frey's maester did with Robb Stark's letters? read more
Maybe Robb had tried sending the Blackfish a letter indicating that Jon Snow was his official successor, but the letter never reached the Blackfish. So it is possible that the Blackfish didn’t actually know. read more
If Robb named Jon as his heir and the Blackfish knows this, he might assume that Maege and Galbart approached Jon with the will, and Jon turned it down to stay at the Wall. I don't know if he knows that the will has yet to emerge from the Neck. read more