If either says no, the flight is grounded.
- finds a maintenance issue
- if there are bomb threats or suspected terrorists are on board
- doesn't trust TSA was thorough
- if there are problems at one of the regional ARTCCs that control airspace a flight path traverses
they can ix-nay the akeoff-tay.
What's key is that this is an occupation that is regulated by FAA licensing, but it doesn't really have a recreational counterpart, so there aren't gazillions of dispatchers to take over for those being 'overly' cautious...