Well, the dispatcher thing is mainly a US thing. In EASA land the flightplan is usually prepared by a computer without human involvement and no active flightfollowing is being done, in the biggest airline in europe it is actually technically impossible as RYR doesn't have ACARS. It is the commander and the commander alone who decides about stuff like extra fuel and alternate change, preflight and during the flight.
Of course, a rerouting preflight, for whatever reason, would require a new OFP and would mean that someone has to tell the computer to do so, which is some person in any kind of operation center.