] I believe (but I don't have the reference with me so I may be wrong) that in the Middle Ages, any degree of consanguinity (up to 6th cousins!) meant that marriage was prohibited unless you got papal dispensation. Since nearly all the royal and noble houses were inter-related, this meant that the Pope had to give permission for an awful lot of proposed matches.
Linden, I believe that you are correct, though in Henry and Catherine's case, I am not sure if there was any shared blood (what a great word, consanguinity), it was more her status as Henry's brother widow that prevented the match.
I think the Popes were handing out lots and lots of papal dispensations to the royals. But then again, since they were busy keeping their mistresses and children in line, they were probably weren't too concerned about a little mixed blood. A little gold always does wonders!