but I have to believe a large majority are more interested in getting the best overall candidates for grad school, and this would be especially true for recruiters looking for grads to hire.
As you said, there are more BYU grads at elite grad schools. If you graduate from BYU, recruiters and admissions officers expect that you are a better student than if he graduated from Utah. This is why a degree from BYU is worth more. It groups you in a more elite cohort. as others have mentioned, there is a lot more recruiting going on of BYU graduates for this reason. That makes for more opportunity.