As someone who has spent the last few years working in the fundraising departments of both private and public educational institutions, I can say that I have NEVER heard a donor, even at the highest level, make a donation with a stipulation being that they would be directly involved in the hiring process of new faculty. There are certainly perks that come from being a major donor; your name on the side of a building you helped fund is the most common, but frequently major donors will also be asked to serve on the board of trustees. However, serving as a boardmember is still a long shot from asking to have hiring control over an entire department.
It's naive for people to think that major donors don't get preferential treatment. But it's equally naive to think that because someone made a large gift, they should be given managerial control. There's a reason that development offices refer to these things as "donations" and "gifts;" people who give them shouldn't expect to get anything in return (apart from the tax benefits of charitable giving).