Kevin,
in Australia I always bury it. With almost soil moisture for most of the year, it will take far longer to break down as there will be less microbial activity than in more temperate areas. However I try to pick a fertile spot rather than baked, bare open ground. If its a region with Dingos present I usually bury it deeper(though this will reduce breakdown time even further), and sometimes put a rock on top, as they might want to dig it up-though in places where I return often I haven't seen this happen yet. Animals in the USA might be a bit more tempted. If they dig it up…more luck to them…and it will no doubt break down faster then. The toilet paper is an issue though, and in rockier areas I sometimes burn it. Even though the chances of someone ever coming across it are practically nil, it is unsightly.
I would be interested to know if anyone does smear, and how they get the courage to do so! I don't think I would enjoy that myself. I think I'd rather just do it on the ground. Plenty of animals do!
Happy pooping,
Adam