The person who first came up with the phrase, "No smoke without fire", and the people who continue to use the phrase again and again, fall into two categories:
(1) Very naive people with very little real life experience
(2) Intelligent but immoral people serving their own personal goals
I say this because anyone who has lived life a bit, in particular in caring roles or in roles of authority, will know that false allegations are just as common as true allegations.
I mentioned in another thread here a few months ago that I sat in a police station in the UK a few years ago, and I was discussing a few matters with a police officer sitting across the table from me, and the office said to me "We receive more complaints of sexual assaults that didn't happen, than did".
The phrase "No smoke without fire" is total nonsense. For thousands of years, communities of humans have been composing accusations against each other, some of them 80% true, some of them 50% true, some of them 20% true, and some of them 0% true.
People tell lies and compose life-changing allegations against other people. I suppose the only saving grace in it all is that people in positions of authority tend to be well aware of this trait.