You are quite right, but so is Aizoon when he makes the point that support for the NSDAP was at its highest in Catholic areas of Germany. And let's not forget the informal Catholic clerical network which helped smuggle wanted war criminals to South America.
The 1930s and 40s were a very polarised time and for the Catholic hierarchy Fascism, which allowed a degree of religious freedom was infinitely preferable to Atheistic Communism.
I think the Church needs to come to terms with its rather cosy Co-existence with fascism - particularly in Italy - during the War.