I don't know that it would burn fuel any faster. I'm assuming that the fighter would be exerting an equal amount of force with scoops closed or open, but with scoops open there would be a terminal velocity, with the scoops acting sorta like a parachute.
Running out of fuel, he probably wasn't able to use afterburners...
Actually, about that, what do you guys think fighters use for afterburner fuel, since it obviously isn't replenished by the scoops. Do (fusion powered) fighters maybe have a small supply of anti-protons that can be injected into the fusion core for boosts in thrust? That could work, and although more energy would be generated as well, more power would be needed to confine the plasma, which would explain why afterburners don't generate any additional energy to recharge weapons/shields.