Of course he’s likely to be quite wrong about that, no matter how strongly he insists this isn’t the case.
But even were it the case, in situ C14 generation is a known fact. It has been shown that even several hundred million year old samples contain non-neglible amounts of intrinsic C14. That C14, however, turns out to be continously generated by (among other things) neutron radiation from nearby radioactive elements in the rocklayers between which the carbon of interest(be it coal, diamond, natural gas, tars, crude oil or whatever) is found.
It was something of a mystery for a time why such old carbon sources contained C14 as it was thought (correctly) that the cosmic radiation responsible for generating atmospheric C14 could not penetrate the crust to the depths in which coal, oil, diamond and so on is found. However, in calculating the expected C14 contents of ground fossil hydrocarbons, geologists had apparently neglected to consider intrinsic neutron radiation generated by the slow continous decay of radioactive isotopes usually found in the types of rocks where one also find fossil hydrocarbons(1):
A PhD thesis(1) was written a few years ago in which it is shown that intrinsic C14 production by neutron radiation is unavoidable and in fact does fully account for the observed levels of C14 in (for example) fossil hydrocarbons:
This could account for the misleading carbon ages Snelling declares with great and irrefutable conviction couldn’t possibly be due to contamination in his “carbon dated” fossils.