Is that really true? I believe that the issues is easier to see with the lens cap on or shining a flashlight onto the top screen, but the effect is always there, just not as noticeable.
Sure light will leak into the metering system, but it already does through the viewfinder, and that's a commonly known occurrence. What was the fix? Check your camera neck strap and find that rubbery thing. Yeah, that's a viewfinder cover. Additionally most cameras metering systems are calibrated so that the light leaking into the viewfinder from around your eyes when your shooting is broad daylight in negated.
Canon, Inc. has issued a similar Canon EOS 5D Mark III service notice (Google translation).
Canon, Inc. adds that a "dark environment" is likely to be:
1. If you have installed the body cap
2. If you attach the lens cap
I've been asked if I am going to send my 5D III in for service. My answer was probably, but mostly for resale purposes. But I will not likely send it in anytime soon.