Between me and a red box, there is a wall with a hole. I see the red box through the hole, and therefore know that the box is red. I reason, however, that I might have instead chosen to sit somewhere else, and I would not have been able to see the red box through the hole, and would not believe that the box is red.

This is a more realistic, and hence better, version of the counterexample that I gave in my ETA to this comment.