I haven't heard anything about Asa Rich being captured and hung. John B. Kennamer's scout company was never mustered into the Union Army and left virtually no records. The men raised their right hands and were sworn in by Col. Lyon of the 13th Wisconsin Infantry in 1864. They were issued uniforms, mounts and weapons, but never put on the payroll. After the war, in May 1865, they were simply verbally discharged and told to go home! (They only numbered around 30 and weren't really expected to do much fighting.)
John B. did succeed in getting recognition for his company some years after the war, however, and the members received soldier's pay for the time they had actually served. I think this was in 1869. Asa Rich's name is among those who served. As far as I know, none of Kennamer's men were killed or died during their service, though Kennamer himself was once wounded. (He was a big man and sort of hard to miss.) Relying on memory, Rich did not serve more than a few months in Kennamer's company. Maybe he was killed after the war and his widow got his pay? There was a lot of bitterness left by the war, and sometimes the killing went on even after it was over. Just as Kennamer's company had never really been mustered into the Union Army, some of their opponents were equally unofficial Confederate "home guards". Shooting of prisoners was not unheard of between the less than regular units, though Kennamer's Company had a pretty good reputation compared to most.
I know of a Captain John Sparks from Sand Mountain, who had deserted the Confederate Army to form another Union scout company, was tracked down and hung from his neighbours not long after the war. Could Asa Rich have left Kennamer to join Sparks? Sparks company was reported around Larkinsville, AL in January 1865.
You can find a roster of Kennamer's Union Scout Company in The Kennamer Family genealogy book, which has been reprinted. It is taken from the application for payment for wartime service and does no more than list names and number of months served.
p.s. John B. Kennamer is buried in the Kennamer Cemetery in Marshall Co., Alabama. Even though that war has been over for more than a century, there still seems to be a bit of friction between the descendants of Kennamers who fought on opposite sides. The family was split right down the middle.