Not even the Catholic Church believes that anymore. Didn't you read any of the Vat II pronouncements?
Here's how it really should be said: All those who are saved are saved through faith in the shed blood of Jesus Christ. When they believe, they BECOME part of the universal church, the Body of Christ. So, no, no one is saved through the Catholic Church. The Catholic Church cannot save anyone, only Christ can do so, and he saves by grace through faith in him.
The Body of Christ and the Catholic Church are the same thing.