That might be true for you, but it's not true for me
Dawkins retorts, "You mean true for you is different from true for anybody else?"
In this response, Dawkins means that to say something is "true for you" is to deny the existence of facts independent of anyone's beliefs. If O'Reilly's statement is a true reflection of what he thinks, he must necessarily reject of the concept of objective realities (i.e. facts) and dismiss methodological empiricism (i.e. observational science).
This is an untenable position, if applied in general, as most of what we do as a society (especially in relation to our use of technology, though not limited to such) relies heavily on our methods of scientific investigation producing increasingly accurate results.
Though O'Reilly's statement itself was likely made without consideration of its implications, the argument in general infers that the person considers his own a priori reasoning and intuition more valid a foundation for belief than reason, empirical evidence, and scientific investigation. It is supreme arrogance to put one's own uninformed beliefs above the entire body of investigation by those much more experienced and qualified than oneself, when one has no contrary empirical evidence and has done relatively little investigation himself.