Danny was the guitar player in Don's band, but I'm not sure he played on the records. I know Kenny Malone played drums on most of Don's recordings, and his producers (Allen Reynolds early on and later Garth Fundis) pretty much used session musicians.
I did a couple of shows with Danny in the past few years, and he told me about how "Tulsa Time" got cut. He wrote it when they were snowed in at a motel somewhere (Denver maybe, or it could've been Tulsa). He went to Don's room to play it for him, and when he walked in Clapton was there - he apparently was playing in the same town/different venue and was snowed in as well. After they played it, Clapton and Williams argued over who was going to get to record it....both of them wound up doing it.
I'm not sure how I would've reacted to Don Williams and Eric Clapton arguing over one of my songs!