The cheapest available option for many students is a school health plan administered by Deseret Mutual Benefit Administrators, which, like the university, is owned by the Church of Jesus Christ of Latter-day Saints.

That plan limits annual benefits and doesn’t cover birth control — provisions that would violate the Affordable Care Act, but for a little-noticed Obama-era exemption for universities that fund their own health plans. It also has a $1,608 annual premium for an individual.

The university’s new policy was set to take effect Jan. 1, the same day Idaho will expand Medicaid to cover 70,000 low-income residents, including some college students. The state expected that about 2,400 people in Madison County, where the university is, would sign up for the program.

Connor Pack, a 26-year-old student on Medicaid, said he was “so incredibly overjoyed” to learn that the school had called off the policy change. “I no longer have to worry about being able to pay,” he said. Mr. Pack, who works three part-time jobs in addition to his studies, was uncertain he could afford the premium and was considering reaching out to his family for help, he said.

While Mr. Pack is grateful that the university will continue to recognize Medicaid, he said, the experience has changed how he thinks about his school.