Even if that was the case, the driver should've pressed the brakes which would've overrode the accelerator.

If it's anything like the e-pedals used in Subaru and Honda vehicles, they should have two different independent position sensors in the pedal. The ecu monitors both, and the value from both must match. If there is a discrepancy, it uses the lower value or zero. So it's extremely unlikely the pedal could malfunction in a way to show 100% pressed.

But I don't know if Tesla does the same.

Driver claims he was passed out, so his account isn't necessarily conflicting with the pedal being pressed.