I am not detracting from Schindler. But neither should we denigrate Pius XII who did more than any other single human being during the war--more than FDR or Churchill, for instance--to save Jewish lives. He did grow silent eventually. But this was because he wished to deflect attention from himself in order to protect the lives dependent on him. Ironically, this became the handle that his enemies used later on to smear his reputation.
But it would be wrong, as you are suggesting, to suppose he was "just doing his job". He went far beyond what was merely required in the name of justice. For instance, since the food refugees were given was necessarily of the coarsest fare, Pius himself refused anything other than what they were given to eat. This illustrated, I think, how closely he identified with those he was hiding, despite the extraordinary danger involved. His own palace basements were packed with thousands of Jewish men, women and children.
It is well-known he was instrumental in saving around 800,000 lives. But did you know that documents recently released indicate that he pleaded with the President of Roumania, then under Nazi rule, to stop a shipment of almost a million Jews to Auschwitz? He worked behind the scenes continually to rescue those being hunted-down. In fact countless lives were saved by this means alone--in addition to those the Pontiff was hiding. The truth about all this is finally getting out--thanks to some Jewish and Catholic scholars--but very belatedly, in my opinion.