Non-profits are businesses--businesses with a privileged tax status.
It is possible to set up a non-profit business such that the money that comes in goes out through different ports than the ownership outflow pipe. A typical setup for a corrupt non-profit is for managers of the business to earn above-market salaries, and to own for-profit businesses that "compete" for service contracts with the non-profit entity.
For example, Jack Grift establishes a non-profit charity for orphan children with fantods. He works the circuit and manages to fund it to the tune of $1M per year. He leases a nice office space in a building owned by Jack Grift AAA Office Space, and contracts with Jack Grift Janitorial Services to empty the trash can, and sets the charity's salary for CEO at $250k/year, and Chief Revenue Officer at $100k/year, plus a bonus of 5% of incoming donations. Jack, of course, holds both positions. He gets $250k as CEO, $150k as CRO, $100k as his own landlord, and $50k for taking out his own trash. He rolls $440k into uncapturable overhead, marketing, and fundraising efforts, and still has $10k left to supply orphans with copies of both Huck Finn and Tom Sawyer.
The finances of universities are even more obfuscated, but it is undeniable that some university employees have the power to spend the organization's money for their own personal benefit. Catered faculty luncheons. Campus beautification in and around personal offices. Settlements from the university to forestall civil suits based on personal indiscretions. Premium parking spaces. These expenditures may, in fact, be justified by the mission of the university, but it is impossible for me to audit any given university's accounting books to make that determination for myself before deciding whether I want to give them more money than they demand on their invoices.
There are a lot of outflow pipes for business revenues. Non-profits only close one of them.