I was doing some hot seat experimentation today to better understand the hide and detect processing.
I noticed that turning FOW off or on does not have an immediate effect - you still need to process a turn in order for a change in options to have an impact.
Now, I imagine that the FOW option does not act as a dynamic filter upon the map, but instead as a flag to determine whether the FOW algorithm is processed during the coming turn. However, this behavior is counter-intuitive, since many games which allow you to turn FOW off and on, immediately display the result. (Perhaps, at least, the rollover text should say that "Changes to this option will take affect when the next turn is processed.")