[xjcsa]

When Kristol questioned this new smear tactic, Brit incredulously suggested that this is something he found on his own.

That's not what the word means. "Incredulous" here is a description of the reaction of the viewer, not of Brit's speaking manner. Words that would work include "incredibly", "unbelievably", and quite a few others.

[Mr. Thorne]

I think it's being used to describe Brit's reaction.

I didn't see the show, but from the description ('Kristol questioned ... smear tactic'), I would assume that Kristol made some comment or accusation to that effect, and Hume was incredulous (disbelieving, expression of disbelief) that BK would infer he was involved in a smear campaign.

IMHO, of course.