Lets say I own a hot dog company and have Scrooge McDuck level money that I have grown tired of swimming in, so I want to waste it on football players to ensure the team I watch for 20% of Satudays in a year is at least mildly competitive.
I find a good recruit and tell him- 'young man, I will pay you $1MM if you come to State, are available to play in at least 80% of games, are not arrested or charged with school violations, and end the fall semester in good academic standing. Additionally, a single picture of you eating one of my company's hot dogs will be taken and owned by the company.'
Who knows if recruits would agree to that, but it would be an endorsement contract that is not directly initiated or managed by the school.