If we were to eat them, surely some amount might end up as soil, but digestion and respiration means that a fair amount of the pig ends up being pumped into the atmosphere from our lungs.
You can think metabolism as a sort of intricately complex burning ritual.
Respiration is based on metabolism and the overwhelmingly prominent elements in human exhalation (exclusive of preexisting atmospheric components) are carbon (as CO2) and hydrogen (as H2O), neither of which are likely radioisotopic components of contaminated food.
Cesium would be excreted as solid waste, winding up in water treatment plant sludge.
For combusted carcasses, absent particulates (which could be largely trapped via scubbers), that would likely wind up principally as ash.
I was thinking that the complaint was primarily about the CO2, but your comment makes me realize that they could have been concerned about the radiation aspects in the air too...
Radioactive boar flesh, as with all other biomass, is already in the biosphere, that is, it is not fossilised carbon being reintroduced. Contributions to increased greenhouse gasses would effectively be net zero.
(Note that non-combusted boars are already expelling CO2 through respiration, as well as more potent gases such as methane through metabolism and decomposition of solid wastes. Methane production through human livestock is among the concerns of climate forcing, though I suspect wild boar populations are sufficiently small to not have a significant impact.)
You can think metabolism as a sort of intricately complex burning ritual.