I think you're reading way too much in this. Were most of Pius XII's teachings weekly worded? Absolutely. Should he have stood up more strongly against the errors of the day? Absolutely. Was he a heretic? Hardly.
There's no other way to understand "according to the flesh". Pius XII CLEARLY refers to the brotherhood of man (since we're all children of Adam and Eve). Christ died for the sins of all. He took the sins of all upon Himself. Therefore, Christ on the cross was taking the place of and standing in vicariously for each human being. Therefore, Christ was united to each human being in some way.
So the Dimond brothers attack John Paul II for having taught that Christ was united "in a certain way to every man." In point of fact, He WAS !