I've done as ST in the past, but like MT says some of the paper is harder to completely burn. A Solo Torch Bic lighter helps with that though. It does take a while to finish and monitor the job and as stated the chance of embers made me think there was a better way.

This last trip I carried a small old drink mix container marked with a scull and crossbones for used TP. Later I burned TP in a good hot fire. Seems to work for me. I wouldn't think of leaving unburned stuff for others.

I'd like to believe the critters are digging up the TP, not just careless people. Dog owners know they can't keep their pets out of the pooh.