When dealing with privileged appointment, the ethically justified standard is Suspect until proven Innocent. Innocent until Proven Guilty was only ever intended as a standard for government-mandated censure of basic rights.
But the question is
should it be? The reasons that it exists as a standard for government mandated censure are very good ones and those reasons don't change when the censure is coming from someone else.
A person's life or career getting derailed because of an accusation is a very serious thing and standards should be high for that sort of thing.
Yes, it should. As I've pointed out a few times, it is all about what is being given or taken away. When something is being given, there is always the question of "is this person qualified (to be given the thing)?"
Note that the standard is a positive claim: that they MEET standards. This same expectation exists when doing things that exclude people forcefully from normal society: do they MEET the standard for being improsoned, etc.
When asking if someone meets a standard, it must be beyond doubt to the extent that the standard protects some level of trust.
Let's apply a little Fourier transformation to the problem: You don't execute a program on your computer in admin mode unless you are sure it isn't infected. Note that the standard isn't 'as long as there's jus a little doubt as to whether it is a virus'. You aren't looking for programs that MAY not be viruses when you want to do a thing, you are looking for programs that ARE NOT viruses. And when dealing with people and organizations, it is much the same: you don't look for people who MIGHT not be child molesters to look after your children, you look for people who most assuredly are not. Of course, it also is not appropriate or acceptable to do a background check for possession of marijuana when hiring for a job pushing fries across a counter, or for looking at Violation of Curfew charges when considering positions at a software engineering firm for a person in their 20's. Or once someone has completed their rehabilitation, that brings in a whole new dynamic.
The point is, when you seek privileges, the burden is on you to prove you will not abuse them, just as when the government seeks to revoke rights, they must prove you DID abuse them.