I'm afraid I'm not convinced.

Was the influence of the test/measurement equipment taken into account?

I suspect without the presence of the camera, etc., that the light may very well have stayed on.

Of course, after a couple of bottles of vintage port wine, the "operators" could have botched the experiment in countless ways.

To add some corroborating evidence, I would suggest measuring the line current to the "Frige" to see if there is a drop of about 1/3 Amp when the door closes (corresponds to 40 Watts change at 120VRMS).
My 1974 Model Sears #62741 "Coldspot Frostless Spacemaker Refrigerator-Freezer" is equipped with its original 40 Watt appliance bulb and does in fact exhibit this differential current change (using my Radio Shack MICRONTA AC V-A Meter); but even this might not be enough evidence in itself.

Review the "Schrodinger's Cat" parable to appreciate the difficulty of proving anything based upon empirical measurements. here.

I believe the latest work on "Quantum Nonlocality", which involves perceptions of signals propogating at speeds far greater than the speed of light, may finally allow for precision measurements/tests to occur without affecting the object being measured/tested.

But for now, I'm still wondering if that Fridge light is really off