I say this as a fan of BYU that has experienced several years both inside and outside of Utah (and both during and prior to independence). I'd say the primary reasons Utah-based BYU fans don't care for indy while non-Utah based BYU fans love it are as follows:

1. Utah based BYU fans care way more about their team compared to the UofU than non-Utah fans and way less about nationally televised games. In terms of seeing the game, the national exposure makes no difference as Utahns as they could always get the games (mtn, espn, etc.). They also care about the comparison because fans inside Utah get Utah Media (Utah sports talk radio/newspapers/newscasts...blah) and the Utah media loves to stoke the rivalry fire for ratings. Also, Utah-based BYU fans have a huge number of UofU fans around them on a daily basis. So a lot of BYU fans in Utah are kind of luke warm on the team right now after so many straight losses to their rival followed by a 2 year rivalry hiatus. Add in the fact that Utah is in the PAC-12 and BYU is a mere independent and independence is a net negative for in-staters.

2. Fans outside of Utah care way less about the UofU because they aren't dialed in to Utah media nor are they surrounded by Utes at work. They also care way more about exposure because they can actually watch the games and feel connected to their team. Ever lived in NYC or DC and looked over the BYU schedule hoping to snag a few games? I have, and independence is about 1000 times better for the East Coast Fan (the MTN was virtually impossible to get in some locations for several years).

3. One other interesting thing is that Ute fans have an annoying propensity to bring up their BCS bowl wins as evidence of why they belong in the P5 and BYU does not (ala, the "Pac-12" country signs), which causes some insecure BYU fans to over-value the post season and undervalue the actual season. Even when I lived in Utah for several years I did not understand why people would want to trade a whole season of great football games against the likes of Texas, Boise State, Virginia & Houston, and replace it largely with a bunch of awful football teams just to get an auto-bid to one NY6 game. There are some real scheduling benefits to independence (even though these benefits have been somewhat reduced by the ACC and SEC's policies that basically destroy any incentive for its teams to play BYU).

Again, I've worn both shoes, but I definitely prefer independence to the MWC or AAC and if I lived in Utah now I'd have season tickets.