Part of what they're set up to do is protect the public from bad attorneys and bad doctors, because attorneys and doctors are placed in positions of trust. If lawyers and doctors are committing crimes, then they may not be able to be trusted, ergo they should be punished both criminally and by the state bar/board.
The NCAA is not set up or intended to protect the public. They are intended to make the sport fair. Punishing criminal behavior that doesn't affect the 'playing field' isn't their area, and frankly I don't think they're qualified or cut out to get involved.
I know why they did. Outrage. But I don't think they should have.