Because having some random unknown woman with some unknown mission serving you is perfectly fine. Dude was wary of her, but somehow just because she one-sidedly for unknown reasons decided to help you, there's trust. Just how an enemy of your enemy is not your friend, just might have a common goal in some way, without knowing about the other side, it's impossible to even guess what their general goals are, so any trust that is built is just a convenient alignment of goals.