Why don't you play on the safe side..Instead of reading and taking notice what every different person says, Phone Canon and tell them what has happened. Peace of mind is Best thing. 5DMkIII is not a Cheep camera. So Phone them up.
There is no way I'd do anything but this with mine. I couldn't afford another, so I'd rather send it off to be checked and have no camera for a month, rather than always have the stress of knowing it could totally fail and let me (and others) down when needed.