These are either employees, or they're amateurs who are here for education.
Can they not be both?
No, they can't. Once one is paid, they are by definition a professional and national and state labor law applies to them.
If this player were an employee, Pittsburgh could have had him sign a non-compete agreement that limited where he could sell his services in the event that he decided to leave. Non-competes are generally pretty bad for the economy in my opinion, but at the very least there would be some legal rationale for that sort of decision.
As things stand now, the NCAA insists these are merely students. Are academic scholarships binding in this manner? Is there anything to restrict a graduate of Ohio University from choosing the graduate school of their choice? Can anybody make a reasonable case that there should be?