Frank, I agree. I suppose there might be
some reason why someone might want to tether himself to his float (loss of float? need to keep floatation nearby?), but to belt himself in - that's hard to understand.

Sounds like, as you surmised, that having been belted in, when the tube overturned, he couldn't right the tube nor release himself to get to air.
Relating to the thread discussion on PFDs, not sure they would have helped him either. I wouldn't think the buoyancy of a PFD would be enough to offset the float tube's greater buoyancy.
Really a sad story . . .