Child molesters need access to children and privacy. Anyone with a key to the building has access to it 24/7 and therefore has access to children whenever they are in the building. Similarly, anyone with a key has privacy. A person can enter the building with a child when no one else is in the building or even if other people are present, they may be able to enter the building without being seen. And, a person with a key may have access to locked portions of the building.
The Vestry is responsible for setting or overseeing the policies and procedures that are used to prevent child sexual abuse. These may include background screening requirements, who has keys to the building, the supervision plan for children’s activities, etc. If the members aren’t trained, they will not know or be able to evaluate whether the policies and procedures are adequate.
Your diocese may have a policy that specifies who is required to be trained or have background checks for diocesan personnel and activities and also for congregations. If the diocesan policy doesn’t apply to congregations, then the congregation through its Vestry decides.