That will be true in most cases, but not all. Some people revealed in a background check will pose a significant risk and indeed some criminals who would have appeared in a local register have reoffended (sex crimes and otherwise) and killed, raped, mutilated, etc..

If a check reveals no known risks, would that make you paranoid? I suspect not. If it reveals only one of your neighbours was convicted of a sexual offence, you check the court records and find that the offence was underage sex when they were a minor - wouldn't that assuage your fears somewhat?

Knowledge is power but you do have to use it wisely.