With a long enough runway, any aircraft could take off at Flaps Up. After all, they CLIMB flaps up don't they? Most just aren't certified to do so, as there is no advantage in doing so as opposed to using slats and flaps.
The reason there have been accidents is because there have been inadvertent Flaps Up take-offs, while using the calculated Flaps/Slats at takeoff settings V speeds, thus trying to get airborne too slow for the actual configuration.