This sounds like a variation on Berkeley's argument for immaterialism.
A materialist - or more accurately a physicalist, but I'll continue using the word materialism - would argue that materialism is justified based on the fact that we can only observe material objects and events. Therefore we can cannot claim that anything other than material objects and events exist.
A simplified version of Berkeley's argument goes something like this:
- When we speak of observing material objects, we are referring to the sensations we have of those objects.
- Sensations are ideas, they exist in the mind.
- Therefore material objects are ideas.
So the argument of your radio host could be that: If materialists are justifying their position based on sense data, then they are already pre-supposing that mental (non-material) objects exist in order to be able to do so, ergo they are presupposing that materialism is false in order to justify materialism.
To quote Berkeley:
But say you, surely there is nothing easier than to imagine trees, for instance, in a park, or books existing in a closet, and no body by to perceive them. I answer, you may so, there is no difficulty in it: but what is all this, I beseech you, more than framing in your mind certain ideas which you call books and trees, and at the same time omitting to frame the idea of any one that may perceive them? But do not you your self perceive or think of them all the while? This therefore is nothing to the purpose: it only shows you have the power of imagining or forming ideas in your mind; but it doth not shew that you can conceive it possible, the objects of your thought may exist without the mind: to make out this, it is necessary that you conceive them existing unconceived or unthought of, which is a manifest repugnancy. When we do our utmost to conceive the existence of external bodies, we are all the while only contemplating our own ideas. But the mind taking no notice of itself, is deluded to think it can and doth conceive bodies existing unthought of or without the mind; though at the same time they are apprehended by or exist in it self. -- Of the Principles of Human Knowledge