>I think, if someone is holding down both the accelerator and brakes

...which is not something that happened in this case in any way, as far as we know.

According to Tesla, "due to the terrain the accelerator may or may not disengage when the brake is depressed".

Not "due to the driver holding down both pedals", but "due to the terrain".

(The driver clearly says that he was not holding down both pedals, too).

I could be misremembering, but I think I remember Teslas having a feature that would apply slight torque to the motors when braking on hills to prevent the car from rolling backwards when switching from brakes to the accelerator.

I wonder if this was a malfunction of the system that detects the car being on a slope which caused it to accelerate forward despite the brake being pressed?

There might be some conditions where it didn't work exactly like it should, i.e. when I enter mine and press brake before car booted up and try shift into drive it says press brake first, even when it's pressed already.

That's honestly probably intentional. The car wants to see the brake in both states before it'll boot. If it wasn't quite paying attention (because e.g. it takes a second to start the controller in charge of this stuff) it might've only seen it in the pressed state.