Utah averages 1.55M per national TV appearance and BYU averages 1.06M.
We can debate all we want why folks are watching Utah, but it's inarguable that more do watch Utah than watch BYU. So I don't think lack of viewership is the reason for lack of dirty reputation (especially since if, as you suppose, they're all opponent fans they would be more attuned to notice that).
There's other reasons (not necessarily laudatory towards Utah or negative towards BYU) that can explain why they don't have the same negative reputation as BYU, but claiming it's a lack of viewership is belied by the numbers.