@JayHawkFanToo Not a correction, but just an idea: giving secret money to a student athlete could be considered participating in a criminal conspiracy by aiding him (men's bb for this) in committing fraud against the school, the NCAA, the conference, and other schools by depriving all those parties of a fair sports competition. It also subjects the school to potential risks of financial deprivation and disqualification that the donor would know the school is unwilling to assume and has taken numerous affirmative steps to avoid.
I would feel very comfortable in bringing a charge like that assuming that the student athlete has signed documents promising not to do things like this, and that the donor knows or has reason to know this. It would be similar to inducing another to commit fraud--which is what we usually just simplify by calling it bribery, but that may be too encompassing.
Again, off the cuff answer but I am sure it is never as simple as saying, hey, I had no obligation to keep that guy honest!
Like you said, it might be possible also to bring this as a civil suit. There used to be lawsuits associated with divorces where a betrayed spouse could sue the mistress (staying with just the guys in this post) for alienation of affection--basically a tort based on inducing someone to violate a contract of marriage. I am surprised we haven't seen more cases where schools hit with sanctions for illegal benefits to athletes sue boosters for actions leading to sanctions.