That's exactly the reason mate. But technically, under that condition, you would be breaking the conditions of your FAC if you decided to take your 'deer rifle' out specifically to shoot a fox during the day...... but it'd be okay to shoot that fox if you were waiting for a deer..... Why not just condition "no night shooting".
That's not really my gripe though, just a peculiarity. My real gripe is individual forces making their own laws up, and nonsense ones at that like a 243 being unacceptable for foxing but a 22-250 being fine.