You would have to go the the manufacturer approved performance charts for this as opposed to Wikipedia as I don't really know where the author obtained that.
But Boeing published the following airport planning data for the 747:
This chart would be representative of a worst case scenario on a hot summer day (90°F) and calm winds. Even under these conditions, the airplane can still depart using a 7000 ft takeoff roll with an GTOW of 700,000 lbs. Practically speaking, this would allow for a full passenger and cargo complement plus 200,000lbs of fuel, which should enable it to fly 3000+ miles with IFR reserves, clearly enough to reach a suitable airport in the Americas, Europe or Africa.
And it really does work, albeit a little hairraising for the tourists on Maho Beach!
This guy is rotates and gets airborne just shy of the aimpoint markers for runway 9, giving him about a 6000 ft takeoff roll. Ambient conditions and GTOW of this particular flight are unknown.