I checked yesterday and I'd got mixed up about what's "the right way"! I've got DH HR's on and the "right way" presents the non-ramped edge, i.e. the sharp edge, to the direction of travel. That's best for braking as it digs in more.
BUT on my Larsen TT the direction arrow presents the ramped side to the front. That's best for rear wheel traction but I've found is poor for braking.
I don't check the arrows, hence how I got it wrong, but always put the non-ramped edge forward (when looking at the bottom of the tyre) because I want better braking, albeit at the cost of climbing grip. I have tried reversing the rear and it definitely gives better climbing traction but it also definitely reduces the rear wheel grip under braking. I didn't feel any effects on resistance but I'm not that sensitive.
So, in answer to the OP. Yes, some people do reverse the rear. If you check the bottom of the tyre and it has the sharp edges forward then that's best for braking. If it has the ramped edges forward then that's best for traction and probably rolling resistance.