Every other truck in the column immediately stopped when the call was made. Truck 1 was the only one that didn't.

They were all, including truck 1, queued up at the stop line waiting for clearance to cross. Truck 1 received clearance to cross, he began crossing, then received instructions to stop after it was too late.

The rest of the emergency vehicles were stopped because they hadn’t been authorized. Truck 1 started moving because he had received specific instructions to do exactly what he was doing.

I take it you’re not a pilot, controller or someone who has ever worked an aviation radio?

I very much doubt that you know the exact timing of the event. My guess is that you might have seen a video where some industrious editor put the ATC recordings over the leaked surveilance footage, but there is no way that is correctly synced.