I know you are just using Nike/Phil Knight as an example, but it's important to remember that major corporations like Nike are separate from people like Phil Knight. Knight was the founder of Nike, but he's not a majority shareholder and is no longer the CEO. For Nike (or a similar company) to sponsor someone it'd have to go through their marketing budgets, and eventually through their board and shareholders. It would be hard for a publicly traded company to justify major marketing spends like this without ROI. Also, for a company like Nike - they'd have to defend a "payment" to Oregon players to other schools they sponsor. If I were Oklahoma (a Jordan school) I'd be really upset if Nike started giving Duck players $10,000 but not Sooner players.
It'd be much easier for Phil Knight the person (or Kevin Plank, Under Armour founder and former Maryland football player) to sponsor a player individually and pay him/her to promote his book, or his foundation or heck, his neighborhood garden. It's Phil's money, he can do with it what he wants. This is essentially what that Miami booster did.