Navy and Army are independent as well. Even Temple was Indy until a couple years ago. BYU is about as comparable to ND as they are comparable to Temple in that respect. Both were/are Indy, but that's about it.

On the bright side, BYU is leaps and bounds ahead of Temple, but take how much BYU is ahead of Temple and that is about as far ahead of BYU that ND is in their football program. Yes, including exposure and especially national fan-base.