Colleges do tend to suffer for mistakes that their athletes make. People will occasionally fully blame the colleges, they feel that the faculty should do more to prevent mistakes that the athletes make and often get angry when those athletes are still allowed to perform their sport with no consequence because it looks as if that mistake is being let slide. The colleges are expected to take responsibility for the athletes that they are showcasing on their sports teams and that includes their behavior and this is not a new concept, the colleges should be prepared to come under heat for these mistakes, especially if they do not handle it responsibly.
Athletes are often supported a great deal by their colleges. If the mistake the athlete made was a direct result of this support (i.e. he or she skated through exams, did drugs, etc) and made this "mistake" over and over again simply because the college turned a blind eye to it, then yes, the college should pay. If, however, it was a one-time mistake and the college handled it appropriately, then there is no need.
They're going to make their own decisions and as long as the coach handles the problem appropriately and doesn't just sweep it under the rug then that should be good enough. If the mistake keeps happening tho and the coach's punishment doesn't get harsher then that's when it becomes a problem.
Although an athlete plays for a college/university, the athlete is still a single athlete and should be looked at as such. Athletes, although blessed with incredible skill and talent, are still human, and as a result make mistakes. Now if the school or any organization has a hand in perpetuating that mistake and or somehow is complicit perhaps by not bringing the mistake, as well as how to avoid it in the future, to the athlete’s attention, that is a different story. However, to have a situation where a college/university was free of any error and then say an athlete’s mistakes should be placed on the school its self, is not fair.
When an individual chooses to make a mistake on a grand scale he or she should be punished individually. Every college has rules and depending on the mistake said individual makes the institution should have rules in place with disciplinary action. The athlete could perhaps lose a scholarship or not participate in anymore athletic activities.