Here is how I like to think of the way in which God guides the Church in its teaching:
Suppose for a moment that I have divine, or at least superhuman powers. You want to drive from Boston to Los Angeles but are a graduate of a U.S. high school and are utterly ignorant of geography. You ask for my help. I say: "My son, have no fear. I will be with you." You say: "But I have no idea which way to go." I say: "Just start driving as best you can."
So you fill up the tank and start driving, taking your best guesses at which way to go. I watch your progress. There are a bunch of different ways you can get to L.A. from Boston, and also a lot of ways to get lost. When I see you are about to make a bad turn, I intervene and shepherd you to a better way. I do this by arranging events that look like normal occurrences. You might come upon a construction crew that makes you avoid the wrong road, or encounter a snowstorm that makes certain roads impassible. Or I might arrange to have something very attractive to you on the right road, like a microbrewery where you can stop for dinner. Maybe you will meet someone who suggests that you visit a certain city for its museums, a city that (it turns out) is on your way to L.A. The point is that you have guided yourself on the trip and I have only prevented you from making mistakes through "secondary causes." Eventually you arrive in L.A. and I say: "See, I told you so." In any case, it's pretty much a miracle that you made it from Boston to L.A. and you are justified in believing in my providence, even if you don't know how I did it.
I think of this when people mention the mundane, political machinations that go on when the Church acts as a body. It sure doesn't look like these guys are inspired by God. But what would such inspiration look like? It's not what the process looks like that counts, but whether we get to L.A.