Here's a thought: in a Good Man Goes to War, the Church is working with the Headless Monks as part of the Silence (in the order sense). But at the crash of Byzantium, the clerics talk about River killing him like it's a terrible crime. Granted this is the Doctor before the future the Silence fears, but TOA/FOD has to be later than GMGTW for them, so their attitude isn't really consistent.
It became obvious to me that this campaign on their part wasn't one that they necessarily expected to win; it was one they embarked on in an effort to avoid the true fixed point in time, which is yet to come.
So given the way the Silence (in the species sense) are hard to remember and think about when they're not there, is the Silence as a whole something that's rewriting time, including the so-called fixed points? (And whose side the Church is on a symptom of that)? As a Time Lord, the Doctor inherits the absolute time of Gallifrey, which, I dunno, maybe reinforces the true history.
I heard somewhere that the Time Lords were supposed to be founded by three people - Rassilon, Omega, and another. I'm betting the Doctor is that other - and if there's anything in the preceding, perhaps if he reveals it, and brings the name back into the universe, it reinforces history in a way it hasn't been since the end of the Time War.