I would never make that argument nor have I even seen it before now, so please don't hold me to that standard. It's a completely ridiculous argument, false on its face, so not something even worth discussing.
Edit: in case the sporadic downvotes indicate some confusion, let me elaborate.
Certainly there is a common argument which involves comparing artificial radioactivity to natural sources. The infamous "banana equivalent dose" is an example of this. But that's fundamentally a quantitative argument about accepting small doses. It's not a general argument for neglecting the danger of nuclear waste in general.
The argument that you should, say, not worry about the dose you get from the americium in your smoke detectors, or the ocean contamination from Fukushima, can be made based on this. That argument is fundamentally sound. But it does not imply that you should go swim to the bottom of a spent fuel pool and hug the canisters, or that it would be a good idea to have a play in the mud next to Chernobyl.
There's nothing fundamentally wrong with making similar arguments for coal. For example, if the amount of mercury contamination in seafood was small compared to the amount of mercury naturally present, it would be quite sensible to argue that coal is not a major problem when it comes to mercury pollution of the ocean. The problem, of course, is that it's simply not true: the natural level of mercury is pretty low, and the contamination from coal power is substantial. When the FDA recommends limiting the intake of seafood for young children and pregnant women, it's not because of the naturally occurring levels, it's because of contamination due to human activity, of which coal is the largest part.