Power of the CoC

How much power do the CoC have over Papacy policy?

The other day in my Hungarian campaign I had been allied to the Pope for something like 60 turns. I did not have many cardinals, (3 at the most), as my priests seemed to prefer heresy to rising in the ranks, but I did not really care because I was seen as very reliable and had an outstanding, atleast, relation to the Pope. I even gave him Durazzo as a gift.

I had been at war with HRE for as long as I can remember, they started it and the only attacks I made on them after breaking their siege of Budapest was a few sporadic sabotage attempts.

Cardinals died and I noticed that more and more of them hail from the HRE. As I have mentioned, my relation to the Pope was fairly good, so it did not worry me that the cardinals came from HRE. Then all of a sudden I get the cease and desist warning about the HRE. Thinking fine, I have not done anything offensive against them other than the formentioned sabotage attempts so I will just continue on the war against the Byz and the 1st crusade (which was not called until well into the 60th rounds..).

Then all of a sudden Venice attacks one of my ports out of nowhere.. And to my great surprise my alliance with the Papacy is in tatters, (venice had allied to them a few turns earlier), our relation had dropped to so-so and the number of crosses were down to 5 from 8 or 9.

Wondering what the hell just happened I saw that the seats in the CoC were distributed like this:

HRE 5 (1 preferati) relations abysmal
Venice 2 (1 pref.) relations so- so
Poland 1 (pref.) (allied through two marriages) (50+ turns, relations so-so)
Sicily 2 (allied so-so, they also have the Pope)
France 1 (allied reasonable)
Milan 1 (neutral so-so)
1 vacant

So 7-5 in favour of my enemies..

This raises the question of how much power the CoC has and the importance of having a majority of the seats. So do anybody know if my fears are true? Have HRE and Venice berated me enough to make the Pope disregard 70 turns of faithful service?