Any time you have organics improperly disposed of (lack of ventilation, too much compression, incompatable waste) it is an issue. When these things break down, one by product is heat, which can start combustion in a slow burn process, using what little oxygen is available, as well as the by products for fuel, thus becoming self sustaining. There are nearby houses etc, which were apparently not informed of the dump when built. The gasses that escape from buring so much crap (such as plastic etc) is the proposed cause of the sickness some of these people like the little boy, are claiming. That is one issue. The fact that if this thing creeps into the nuclear waste, as it burns, will heat up the surronding material, taking either radioactive particulates or gasses up into the air. That would be a bad thing.
Most of the coal burns, like the one that ate a Pennsylvania town, were human started, once they get going, the do become virtually unstoppable, other than running out of coal to burn. Other than usually burning or deforming the ground above, you are correct they are not a huge threat. Put one next to a nuclear dump, I would say it would become a much bigger issue. That is why a lot of us in the NW are concerned with the idiot response to the Hanford debacle, it will soon start leaking into both groundwater and the Columbia river, and this stuff is really nasty.

There is a garbage dump that has started an exothermic reaction, either from incompatable waste or just heat from organic decay. My manuer pile does the same thing, composting on a huge scale with poisoned compost as a result. It will eat its way through and organics, and if it reaches the waste,then you start cooking off any liquids, and the heat may cause release of radioactives to the air. Note the physical issues already being seen in people living nearby. I thought this was a good illustration of just how incompent these guys are, and if this is their level of reaction, just shows how much we have to worry about, as if we don't have enough...