Eh, kind of. Let's say I am up for a promotion along with a few other candidates, and I have a reputation for being a sexist pig in the workplace, while the others are squeaky clean. There may be no concrete evidence, but a couple of people have complained about it.
I don't think it's up to those other people to prove beyond a shadow of a doubt that I'm not fit for the job. In this situation, I think it's up to me to prove I deserve it.
If I can't, whoever is making the decision may decide to err on the side of caution, and that is 100% ok.