That’s a problem if he’s conflating uniform with random. One must ask what if anything a measure of the departure from a uniform distribution means and whether the uniform distribution can possibly make any biological sense. And this leads into the question of just what “active information” is really supposed to mean; I don’t refer to the definition but to the interpretation.
As an addendum to my original questions, I’ll add this: if we accept that some DNA is nonfunctional, i.e. junk, would we not expect that mutations in junk would be “random” by the standard meaning, i.e. with respect to fitness? And wouldn’t the distribution of mutations in junk make a for better comparison than starting with a uniform distribution?