pilsner,
Maybe we're not visualizing the same thing. I think the OP describes the pitcher throwing to first base, and the ball strikes the runner close to (within a catchable distance if F3 were there to catch it) the bag. This is not a balk, because the pitcher actually threw to first base. As long as the pitcher's throw passes over or sufficiently near to first base, F3 is optional.
If the pitcher throws too far away from the bag, then he needs to throw to F3 who has to be close enough to the runner to make a play.