You've put it in a nutshell. That's the problem with quoting only documents from post-1962. They need to be seen in their proper setting and understood in the context of the hundreds of years that went before.
And that is something I only discovered on my own. Sadly, the Catholic educators in my experience are more likely to recommend reading Martin Luther before Pius XII. (I REALLY wish I was using hyperbole to state that, but I'm not.)