I wouldn’t say stopping a car is a reflex action…..
Sneezing or pulling your hand away from a hot surface is a reflex action.
The guy clearly thought he was braking. As above, he was probably just pressing harder on the ‘brake’ pedal to get the desired effect.
In his head he was pressing the brake pedal, but the car wasn’t slowing down. but in his (their) panic, there was no consideration of why they weren’t slowing down.
I did a similar thing at a petrol station years ago in Germany. I pulled in, realised the cap was on the other side and the hose wouldn’t reach around the back of the car as it wasn’t far enough forward.
I half sat in the car with the door open, took the handbrake off and gave the car a shove with my foot. The garage was on a slope and as it rolled I applied the foot brake (but was actually pressing the accelerator – ignition off, so no vroom vroom noises). It wasn’t long before I had gone too far, but was still not stopping. I was pressing and pressing the pedal. I was also getting worryingly close to a car parked side on at the edge of the forecourt where a bloke was checking his tyre pressures. I grabbed the handbrake and the car stopped.
I then looked down to realise that in my half-seated position I’d been pressing the accelerator, not the brake and had to sheepishly start the car up & reverse back to the pump with the bloke who’d been checking his tyres giving me evils….