No matter how deep a background check goes, no matter how thorough the inquiry is into a person's character, no matter how many interviews are made of friends and family, and no matter how many polygraph tests are performed, if a person is given a position that requires some trust there is always going to be a chance that this person is going to abuse the trust. Psychopaths and sociopaths the the scariest of these people because they have no problem with lying, are good at it because they are usually good at being manipulative, are often very well liked by family and friends, and can lie without end like a baby-kissing politician running for re-election and still pass a polygraph test.
Perhaps the problem is in the kind of people being sought for these jobs that require great trust. While a person needs to be squeaky clean to get security clearance, perhaps the squeaky clean requirement is causing the government to choose some from the wrong pool of candidates. My experience has been that you will have a better chance of finding an honest man (or woman) by looking at those who have messed up in his or her life, is genuinely repentent, and has demonstrated through years of clean and honest living that he or she is worthy of such great trust. The gratitude that comes from being given this second chance is an incredible motivator in steering a straight and narrow course through life.