As with almost anything, there is a difference on how something works when practiced by experienced/careful people and when practiced by "yahoos".  The burning of TP under ANY circumstances can present dangers.  More than one forest fire has been started by a rogue gust of wind and burning TP.  That danger is reduced if the burning TP is surrounded by a cleared area, typically the case where a fire pit is located.

There is plenty of air under ground to sustain fire. One of the ways forest fires travel is by burning underground, following a tree's root system.

So burning TP in the fire place I will be cooking in?  Ewwww.  Telling every yahoo going into the park to burn it in a cat hole?  Just asking for trouble. I don't have a solution. 

Except maybe giving everyone headed into Q a cork.  ::)