My daughter works for Intermountain. The LDS does not own Intermountain.
Intermountain’s big hospital in Murray is in a long term contract with UU to provide clinical placement sites for their students. So the LDS Hospital in SLC.
Intermountain may have some smaller satellite sites that can take BYU students. (Intermountain has been expanding by buying up smaller hospitals in Idaho, western Colorado and parts of Nevada.) But there is a national shortage of clinical rotation sites.
All allopathic medical schools are required by the LCME (the national accreditor for all MD programs) to prove that they have sufficient rotation sites that meet LCME standards for their students. COCA (National accreditor for all DO programs) also requires med schools to provide a list of approved rotation sites for their students.
BTW, international rotations are not approved by the LCME or COCA. Nor any state medical board. Students who do any of their basic and required elective rotations overseas will not qualify for a US medical license. (Alternatively, doing overseas rotations may cause them to be considered IMGs–International Medical Graduates which requires an alternative pathway to residency and medical licensing,)
For a LCME accredited medical school, there is a requirement for substantial start up funding (Millions of $$$), plus a requirement for ongoing academic medical research as part of the med school which requires acquiring both faculty and facilities.
If BYU is trying to open a MD program, expect the timeline to be in the 3-10 year range.