throw dirt enough, and some will stick
If enough allegations are made about someone or something, then even if they are all untrue, people's opinion of the person or thing will be diminished.
1759, John Wesley, letter to John Downes, Rector of St. Michael's, Wood Street, read at Wesley Center Online at https://web.archive.org/web/20060903061313/http://wesley.nnu.edu/joh