Smart, affluent Californians are not choosing Michigan over the top UC schools because of academic reputation. As Alexandre notes, Berkeley has an equal or better reputation than Michigan. UCLA, UCSD, UCSB are all fine institutions a Californian can go to for less than half the price of Michigan. Despite this, Michigan enrolls hundreds of Californians each year, with most being unhooked, full pay students. My daughter has a friend in her dorm from the San Diego area, who chose Michigan over UCLA because her family could afford the OOS tuition, and she wanted to go to a school with strong academics, with top level sports/school spirit, in a different part of the country. Michigan fit the bill.
Henry Gunn High School in Palo Alto is one of the top public high schools in the country and provides anecdotal support for this trend. The Gunn HS class of 2016 had about 460 students, of which 104 were National Merit Commended and 46 National Merit Semifinalists. Palo Alto is a very affluent community, so many families are not limited to UC options. In 2016, per naviance, 51 Gunn students were admitted to Cal Berkeley but only 22 enrolled. 69 admitted to UCSD, only 9 enrolled. 38 were admitted to UCLA, only 4 enrolled. In contrast, 46 Gunn students were admitted to Michigan, and 19 enrolled. The “yield” of Gunn students by Berkeley and Michigan was close to the same, even though Michigan is 2000+ miles away and much more expensive. This does not mean Michigan is any better than Cal or UCLA, but for some California families who can afford it, Michigan is the preferred choice.