The provenance doesn’t sound as good as they are saying to me.
There probably is no doubt that Jesse’s Son owned it but he could have bought a bunch of guns and claimed they were his Father’s.
It's tough, and especially so with "Jesse James" guns. From what I've heard, the problem is that Jesse appears to have used several different guns during his career, for one thing. But even so there are way too many guns out there that all appear to have good provenance. Hundreds of guns. It seems so that Jesse's next of kin made something of a cottage industry out of auctioning off pistols that they claimed belonged to Jesse. They can't all be legitimate. So... The market for -real- Jesse James memorabilia is forever polluted. That's probably why that gun didn't sell.