MYTH: Children are usually molested by strangers.
FACT: 85% if children are molested by someone they know. The people most likely to molest children are those who have the most opportunity and access to them.
Approximately 1 out of 3 girls and 1 out of 5 boys will be sexually abused before the age of 18. Persons with developmental disabilities are sexually assaulted more frequently by a factor estimated between 4 and 10.
29% of offenders are relatives; 60% are acquaintances; and only 11% are strangers. It has been calculated that the chances of getting caught for child molestation are approximately 3%. Fewer than 1% of offenders are arrested, convicted and imprisoned.
http://www.hccac.org/abuse/myths.html
This does not prove your fantasy that children are safer with strangers that are likely to be pedophiles than with people who have been investigated and shown themselves over a period of time to be trustworthy. I hope there are no children or even adults depending on you to look out for their safety.