Yes, Zal, that is the general descriptive term of the rural (not just southern) Utah pronunciation. Linguists generally pick one notable pair and then label the phenomenon that way (like the pole/pull merger or the feel/fill merger).
One of my professors last semester was doing some research on Utah English, and this was one of the main features she focused on. Evidently, it's dying out in the younger generations, and it almost never occurs among non-Mormons. Interesting sociolinguistic implications.