That's what they claim. How many altarboys do you have to diddle to lose that claim?
How many millions of poor do you have to feed, billions of prayers do you have to pray, souls do you have to save, to get back that claim?
It's patently ridiculous to expect the Church on earth to be perfect. We are sinners, of course, but it's still God's truth we proclaim, which is perfect. And that's where the authority comes from.