Swallowing the red herring?

There are a couple of different issues here we can address: 1) Your friend's assumption and 2) WLC's use of Bayesian theory as a way to defend a alleged miracle. Let's start with #1.

I would question how your friend knows this—unless he prefaced the statement with an opinion qualifier such as "probably." It is possible that WLC admitted to this kind of "sophist gibberish" as you so eloquently put it, but unless he did, his reasoning for using Bayesian theory would be unknown.

If WLC really did admit to saying that, he is basically admitting to an Argument by Gibberish or perhaps the more specific form, argument by prestigious jargon. WLC would be right that much of science that is used to debunk supernatural claims is generally beyond the intellectual grasp of the layperson. This sounds kinda elitist, but it is more likely than not factually accurate based on the scientific literacy of US. The problem with WLC's line of "reasoning" would be that his opponents who use science are using it correctly—his use of it is not.