I don't know if they can really screen them before anything happens. If they don't have a criminal record, there is really no way to know beforehand. I do think they have a responsibility to act properly the second one of them is found to be abusing a child. I know as a nurse, I am required by law to report any suspected child abuse to the police and I don't see why the church should be treated any differently. I don't see why any adult should be treated differently. As much as we blame the church, none of these incidents could have ever been covered up had the child's parents been unwilling to go along with it. That is a far greater betrayal in my opinion and we tend to forget about it in our rush to bash the church.
Priests submit to at least one psychological screening, if not more, in order to be allowed into the vocation. My father in law is training to become a deacon, and even he has had to be screened. He has seen men from his classes go through the screening only to be turned away for a variety of reasons. It's cmforting to know that there are steps being taken to help protect children from the abuse of authority.
And you're 100% right about parents having a say in whether or not an abuse gets covered up. But, at the same time, I think the church USED to hold a lot of authority over its participants. Most people I know now, view the church as 'theirs', employess rather than bosses. The same attitude of having to listen and obey without question what the church tells you is no longer there. This makes it completely unexcusable for a parent now to help cover up a molestation, but, it makes it a bit more udnerstanding why families in the past would have kept quiet about the issue. It was a clear abuse of power not only over the children, but the families as well in many cases.