One (simpler) explanation is that proving an absence of something is almost impossible, and that attempting too hard would make them look a heck of a lot guilty.
There is a good reason why the burden of evidence is “innocent until proven guilty”, and yes this extends to the (in your eyes) untrustworthy.
Prove to me you never stole candy from a store as a child (or if you did, replace that accusation with any item of higher value until you hit something you did not steal)