I shot an email to Canon, India and below is the response i got. I think it's fair.
As far as we know, this phenomenon does not affect the 5D Mark III in real world shooting conditions. This is a theoretical issue that was present in the 5D Mark II as well, it is just that no photographer shoots under such artich as shooting with a lens cap on, or shooting in total darkness with a long exposure. And with exposures longer than a minute, the 2 seconds of LCD illumination would not effect the exposure to any degree.
We feel that this has been highlighted with strong intent to undermine what is a strong product.
However, to calm the fears of persons who have purchased the 5D Mark III we are offering this service free of charge, and all models shipped after this problem was noticed do not have this problem.