http://www.comune.roma.it/was/wps/po..._the_airports/

The fare includes everything but it's FCO - all destinations within the Aurelian Walls, rather than FCO-everywhere in Rome. I can't read the map very well but I'm afraid the CP is slightly outside this area - it's a matter of a very few meters! - so the taxi should not apply the flat fare, but I see that both the CP website and some taxi company website reports the 40-euro fare for that address.

There's a kiosk ran by the municipality of Rome at T3 arrivals. They provide info about taxi services in Rome (though with limited business hours: 10-18...)
You can see a pic here
http://www.adr.it/portal/content/Fil...y/taxibox2.jpg