This may sound like a technicality, but the University of Michigan’s Board of Regents isn’t appointed by anyone in state government. They are directly elected by the people on an at-large, statewide basis, as provided in the state constitution. That makes them state constitutional officers, and the university’s ultimate governing body. Neither the legislature nor the governor has any significant say in the university’s budget, policies, programs, or priorities, academic or otherwise. As a consequence, there’s much less political interference in the university’s affairs than there is in many other public universities.
The downside of this arrangement, perhaps, is that without political “ownership” over the university, the legislature has been pretty miserly with appropriations to support the university for the last, oh, say, 30 or 40 years. Left to its own devices, the university has developed its own financial model, centering on building a massive endowment (perennially among the top 10 for any college or university. public or private), aggressive and highly successful pursuit of competitive research grants that now exceed $1 billion annually (#1 or #2 nationally, depending on ow you count), and at the undergrad level, heavy reliance on OOS tuition, with OOS students comprising roughly 40% of the undergrad student body. It works for Michigan, and UVA has successfully developed a similar model. Others want to emulate it, but most of them have a long way to go to catch up.