I don't know the deal, but I sorely doubt that the deal is "free" in the sense that Nike gets nothing. Much more likely, they get some sort of cut down the road.
Nike is not a charitable institution. They make money. So it's probably more of a "you don't have to have a debit on this year's budget, and we can nibble out of future revenue streams" than a "here, we're good guys, let us help you with that."
It may be penny wise and pound foolish, but, at the end of the day, for a state school in a bad economy, it's probably politically much easier to say "free" and figure most aren't smart enough to figure out the not-free part, than to openly pay a Madison Ave. company 1 million to design a new logo.
I remember my father working for a corp that had a new logo designed for 1 million. I laughed when i saw it. It was two plain block letters, slightly intersecting. Boring, plain, and could have been done in 10 minutes by a competent 12 year old. They used it for less than a year.