So yes, the faithful can wield reason as comfortably as the non-believer. But the caveat, the sticking point between the "rational believer" or apologist and their heathen counterparts is that little parenthetical phrase up there, "know (or accept)".
An average man might say he knows a lot of things, a very philosophical man might say he knows practically nothing. But most will accept (if only for the sake of argument) that there's a real world, with people in it, and a sun in the sky, etc.
But while an atheist might say "I can't accept there is a god without evidence for one", the theist will say "I can't accept there isn't a god, my God, without proof."
These aren't symmetrical positions. Many atheists would accept above a certain level of proof for one, that some divine or supernatural being exists. If a giant face appeared in the stars, and everyone heard in their own language an impossibly moving voice say tomorrow all the sick will be healed, and then it happened. I am probably not going to stick my head in the sand to a chorus of "maybe they're aliens!"
So what would convince an apologist or fundamentalist that there's no god? Most I've met say nothing would. They start by wanting proof, and then limit proof to a supernatural level of confidence. You see it when someone says of an apostate "they were never a true Christian/Muslim/sub-Genius to start with, no-one who had felt God's/Allah's/Bob's love in their heart could ever walk away from it!"
It's not reason that's playing favourites, it's reality.