That's not true. The goal judge's only purpose is to determine whether or not the puck is in the net. The goal light has absolutely no bearing on whether the goal counts; if the referee determines the puck crossed the line legally before time was up, even if the goal light didn't come on, it's a goal.
If they implemented what I have been calling for for years, the goal light would be used for exactly this purpose, among others. I have been asking for YEARS for the NHL to implement a system based on FoxTrax puck technology that uses a system of sensors in the goal frame to determine if the puck enters the net, and when. This system would completely eliminate 'manual' goal judges, and would automatically stop the clock if the puck completely entered the net. Obviously, it wouldn't necessarily signal a valid goal had been scored...but the play would still be over.
This could also eliminate situations where you know the puck crossed the line, but it can't be proven with conclusive visual evidence.