Doesn't this contradict the idea that god does not affect free will?

That's not the point of the story. The point of the story is that Joe is ignoring the opportunities God is giving him to help himself and demanding that God send a miracle to help instead. The story isn't literally true. It's simply intended to illustrate a point. That's like taking one of Aesop's fables and saying they claim animals can talk so why does my cat only meow?