The jumpman logo and the Jordan brand is a subsidiary company of Nike (the parent company). So while Nike owns them, the Jordan brand still has their own deals/contracts in place with different organizations that are separate from Nike contracts.
In short, while Nike owns the Jordan brand, they are not interchangeable. That's why we have a swoosh and Michigan has the jumpman logo. If Michigan wanted to wear a swoosh they would have to get out of their current Jordan contracts and vice versa for us.