Given a history of consistent propaganda alleging a strong liberal bias in the national media, much of the GOP base would likely be sympathetic to this kind of behavior. If you are convinced that the media is strongly biased against a candidate, you might not have any problem with said candidate avoiding interviews.

This tactic works with the base, because it is consistent with the “they are all out to get us” message. Of course, it doesn’t work with anyone who hasn’t already bought into the whole white christian victimhood meme, but then, they aren’t going to vote republican anyway.