"I'm saying that a person can have faith in God, for example, or they can know God."

Or one can have faith in God, and that faith distorts their perception of an experience.

For example: I have seen several UFOs. Yes, yes I have. I've looked up in the sky and seen things I couldn't identified. My reaction was "Hey cool, it's a UFO! I wonder what it is? Aircraft? Aliens? Weather ballon?"

If I had faith or belief that aliens were visiting this planet on a regular basis, I might have interpretted that experience very differently, and assumed that I had indeed seen the craft those small gray aliens fly around in.

I don't think experience = knowledge. Experience may contribute to knowledge, but experience can be subjective. As "truth" it can only be interpreted on a personal level.

One might get a warm sensation while praying and call it an experience with God. Another might call it heartburn :)