Flight plan is checked for route validity -15 +15. So +13 atc can approve start up. If you had been previously arriving in regulated airspace just before the regulation started (i.e. 1 minute), you would not have been allocated a slot. Delaying the flight would have forced a re-calculation of the profile pushing you into the regulated period (and at the back of the queue) so you receive a bad slot.
Someone calls NMOC and we improve the slot as much as possible, you depart.
Flowman