There is no evidence that the Vatican organized a coordinated, continent wide campaign to save Jews. None. Did individual Catholics and local Catholic parishes save many Jews, perhaps in the hundreds of thousands? Of course. But it's just factually wrong to attribute their actions to Pius himself. And the real story is, if anything, more heart-warming. They saved Jews out of the goodness of their hearts, on their own initiative.
Again, I'm not disputing that Pius saved Jews, and tried to save Jews. I'm disputing the ludicrous figure of 860,000. There's no reason to use wildly inflated numbers to make a case for Pius.
Look at it another way -- 3 million Jews escaped or survived the war. Of those 3 million, most survived because Nazi's either never directly controlled their area (Bulgaria, southern France), or didn't control their area long enough to finish the exterminations (Russia, Ukraine, Hungary etc.) Hundreds of thousands of others fled before the war.
I don't 860,000 Jews, in total, were saved by "anyone" -- much less the actions of Pius personally, or Catholics collectively.
"The Pope depended on the local clergy to thwart Hitlers extermination policy. The book dramatizes one point above all others, Feron states, that the Popes efforts were dependent on the strength and heroism of his churches in each country. Lapide traces the efforts of Roman Catholics to save the Jews and quotes a variety of sources to indicate that Papal Nuncios had received messages from the Vatican to contest the deportation of Jews. Lapide tells how Pope Pius XII sent his Papal Nuncio in Berlin to visit Hitler in Berchtesgaden to plead for the Jews. That interview ended when Hitler smashed a glass at the Nuncios feet. From Hitlers reaction the Pope was convinced that public pronouncements would have sealed the fate of many more Jews. After this incident, in retaliation, Hitler connived to kidnap Pope Pius XII."
- Margherita Marchione, "Did Pope Pius XII Help the Jews?"
If you don't like Lapide, and consider him prejudiced because he was an Israeli diplomat and angling for recognition of Israel by the Vatican (that's the attack I've heard), there's still Rabbi David Dalin to deal with. He took apart Cornwell's book in The Myth of Hitler's Pope. Cornwell, of course, has recanted much of what he said in that book.