I have just read the reference and two things occur to me.
1. The reference describes an object which is chasing another object which is itself moving. This is not the case with the navigation beacons.
2. If the hare is running directly away from the dog (which sounds like what any sensible hare would do) or directly towards the dog (a mad march hare possibly), the dog's path will be a straight line. This is of course the equivalent of the beacon being directly upwind or downwind of the aircraft.