Does the University of Michigan's New Football Coach Need Food Stamps?

The Huffington Post reports:

One of the big end-of-the-year sports-news items was Jim Harbaugh leaving the San Francisco 49ers to become head football coach at the University of Michigan. Reportedly, his salary at the University of Michigan will be $7 million for the first year. If that doesn't sound like the income of a food-stamp beneficiary, then you'd better look more closely.

One of the arguments for shelling out big bucks for Harbaugh is that a winning football team will encourage enough contributions from devoted University of Michigan alums to easily cover the $7 million paid to Harbaugh. Insofar as this is the case, taxpayers are picking up a large chunk of Harbaugh's salary.

The point here is sufficiently straightforward that even a Republican member of Congress should be able to understand it. The University of Michigan is a tax-exempt institution. This means that people who make contributions to the university get to deduct these contributions from their taxable income. Since most of the money the university gets comes from people in the highest tax bracket, the government is effectively paying 40 cents of each dollar that these people contribute to the university, in the form of lower taxes. If all of Coach Harbaugh's $7 million salary were covered by donations from high-income individuals, the government would effectively be subsidizing his pay to the tune of $2.8 million.

Why doesn't University of Michigan want to pay their "fair share"?