Once more for all the worry-warts: this is most emphatically the correct response from Canon, because the "problem" isn't.
To confirm for yourself, find a 5DIII and a dark room and perform this simple experiment for yourself: Put the camera in manual mode at EV 1, the specified minimum light level at which the meter is effective. That would be one second at f/1.4 at ISO 100. Find some place to aim the camera that the meter bug is centered. Turn the top LCD backlight on and off, and the meter won't budge.
You can try it at EV 0, too, and it still won't move -- but keep in mind that you're now operating the meter outside of its specification, so you don't really know if the reading is right in the first place.
At EV -1, it might move a third of a stop, and it probably will at EV -2. At EV -4, it'll probably move 2/3 stop, but, again, at all these settings below EV 1, you don't know for sure what the proper reading really is. Indeed, it could well be that the reading with the light on is the correct one, or neither. That's what it means to be using the meter outside of its specified parameters.
Oh -- and even EV 1 is dark enough that either you're doing slow-shutter tripod (distant skyline at night) and you're not relying on the meter anyway, or you're shooting at insane ISOs and you're not expecting top-quality results anyway.