Because your SHC cases occur in public (rather than all the reported modern cases, which occur in solitude), you're in something of a pickle. However, I do believe that a sort of solution is possible.
As has been mentioned, soft tissue (but not fat) is essentially water, so getting any sort of combustion going is a losing proposition - the body will act as its own fire extinguisher. And somehow replacing the body's water with something flammable, like alcohol, will have obvious and dire metabolic consequences. It's very hard to see how a victim could be walking around with a massive replacement of water with something else.
But let us consider the alternative to soft tissue - bone. The skeleton makes up about 15% of the body by weight, with a nominal density of about 3 times that of water, so it's about 5% by volume. Now, what would happen if bones were (by some wild biochemical weirdness) replaced by a spontaneously flammable substance? Let's take nitrocellulose as a base line. The density of nitrocellulose is about 1.7 times that of water, with an specific energy of ~ 10 MJ/kg. So a 100 kg person with modified bones would have a skeleton comprised of ~ 8 kg of nitrocellulose, with an energy content of about 80 MJ.
Thermal capacity of water is 4200 J/kg-deg C, so raising a kg of water to boiling will take ~ 294 kJ, and boiling that water will take ~ 2.3 MJ/kg, for a total energy requirement of ~2.6 MJ/kg. As a result, ignition of a nitrocellulose skeleton will only destroy ~ 30 kg of soft tissue.
Well, nearly half-way there.
Now let's look at fat. An overweight person might have on the order of 30% body fat (more for women). If, in addition to the bones being replaced with nitrocellulose, the composition of the body's fat were changed to 70% nitrocellulose, you'd have more than enough energy available to reduce the body to ash.
The process would presumably begin with ignition of "bone" at one of the extremities where there isn't much flesh, and the advancing ignition zone would ignite the modified fat to complete the job.
Are there problems with this? Oh yeah. Regardless of the perversity of the biochemical process required to modify bone and fat, at least 2 issues arise. First, nitrated hydrocarbons are toxic. Exposure to materials such as nitroglycerine and nitrocellulose will kill at quite low doses, so how the altered materials would be sequestered without killing the host is anybody's guess. It's magic, I suppose. Second, the modified bones would no longer (without some really serious handwaving) be able to support the growth of bone marrow, and the immune system would go to heck in a handbasket.
EDIT - And another problem - how do you get muscles to attach to the new material? END EDIT
But those are left as an exercise for the reader.