Ah that makes sense. But unless he fathered a child with his hapless Frey pawn of a wife* the Frey claim to Riverrun is much more tenuous.
* He does get Roslyn Frey pregnant in the books; all three are slated for hostage-residence at Casterly Rock after the Riverrun showdown.

"Edmure has a Stark target on his back"
Sorry, not following you there. My recollection was that Edmure was forced into marrying a Frey somewhat reluctantly as compensation to the Freys for missing out on having Robb Stark married into their family. What am I forgetting here?