Yes, I use both hands for painting. I use both hands for many things, actually. Not totally ambidextrous but nearly.
Pondering on the back problem, I'm wondering if it depends (partly; the main problem is arthritis) which muscles are being used the most. Hedging, scything, shooting arrows use big back and shoulder muscles and it's as much about getting alignment of joints right (especially in archery) as strength. Wall and woodwork painting uses hand, wrist and arm muscles more than the big back dudes. Not sure how that would cause strain in my low facet joints but it seems to. They're all connected up, right? 
(Can one ponder something or does one have to ponder on something?)