I strongly suspect the idea of wrapping against the twist is based in a Victorian era assumption of how a patch behaves after exiting the muzzle. If it actually unwrapped around the bullet I'd expect to see horrific accuracy as it added drag while the bullet rotated.
I suspect high speed footage would show paper patches blown to atoms on exiting the muzzle. At least that's been my experience shooting paper patched anything through a rifled bore... not much left down range besides dust. Who's ever recovered an unwrapped patch anyway?
Considering a bullet with a MV of 1200 fps and a 1:20 twist, that's 43,200 rpm at the muzzle. I can't see any paper patch posing much resistance to that centrifugal force. If spin from rifling is enough to tear solid lead and copper jackets apart I expect paper won't stand much chance.
Be neat to see it filmed on high speed.