That leads to situations like Georgia being shocked that there was wrongdoing in its basketball program after hiring Jim Harrick, the guy UCLA fired for lying on his expense reports and who subsequently ran afoul of the NCAA at Rhode Island.
Or Jerry Tarkanian making Fresno State the third notch on his probation belt when he worked there at the end of his career. I'm sure the administration thought its oversight would be enough; and besides, Tark wouldn't sully the name of his alma mater.
If you knowingly hire a dishonest person, don't be surprised when he finds creative ways to be dishonest no matter how good you think your controls are. It isn't a matter of PR. It's the inevitable trouble he will cause.