Keep in mind that "self imposed" penalties don't just come out of thin air. They are actually listed in NCAA guidelines. So the way it typically works is that a joint investigation is done by the school and the NCAA Committee on Infractions. That committee consist of volunteers from various NCAA institutions as well as persons with legal expertise. See link for committee members. http://www.ncaa.org/ncaa-division-i-...actions-roster
Once the investigation into potential violations is complete the offending organization works with the NCAA COI to determine a path forward. There are four different tracks from this stage which can be taken.
The most common of which is a negotiated resolution. This is the most common method used when an offending organization finds wrong doing on the part of the organization. The organization and COI work together on the complete report including wrong doing, penalites etc. There is a defined structure for penalties so the COI and the offending organization have a prescriptive set of rules to follow. There is no appeal for a negotiated resolution. Second most utilized is a Summary Disposition Track where a report about facts and levels is agreed to and a hearing before the COI happens and the COI determines penalties. This is the only track that allows for penalties to be appealed and rarely is an organization successful on appeal.
The other two options involve a lot of time and money and the COI have final say on penalties anyway. Most organizations that choose one of these paths do so because they figure it can't get any worse but they are usually wrong. The COI doesn't take kindly to organizations who they view as being uncooperative.
Here is an example of penalties given to Brigham Young for a booster giving 12K to a student athlete. If the allegations involving little Willy are true expect them to far exceed the below.
Two years of probation from Nov. 9, 2018, through Nov. 8, 2020.
A vacation of records in which the student-athlete participated while ineligible. (2 yrs)
A reduction of one men’s basketball scholarship, served during the earliest possible academic year (self-imposed by the university).
Recruiting restrictions detailed in the public report.
A disassociation of one of the boosters (self-imposed by the university).
A $5,000 fine (self-imposed by the university).
By the way I know the perception is that the big conferences get away with things that smaller conferences get hammered for but that isn't really the case. For example the NCAA COI list 23 major infractions for the SBC and 73 for the SEC (most of all conferences)