They are getting this idea from their interpretation of St. Paul’s writings on the Law of Moses. Verses such as this: 1Cor.15 [56] The sting of death is sin, and the power of sin is the law. Would seem to support this interpretation, but St. Paul says a great deal about the Law vs. Grace that it can be hard to sort out just what he had in mind.
Certainly the Law showed us that we are not capable of keeping it, but it did more than that. God would not have given it to us if all it was supposed to do was tell us we’re sinners. It was meant to show Israel what God expected of them as the People of God–their obligations to both God and man. The Ten Commandments do this, which is why the Church still holds to them.
It’s not that St. Paul did not say that the Law points out that we are sinners, but it’s not enough to say that. He also wrote that the Law was holy and righteous, but that the grace of God supercedes the Law. Therefore it is not the Law that saves us, but God’s grace.