I would have to agree with erin. It is not the fact we want to cover our eyes, it is much more to do with covering your mouth which is either gaping wide open or muttering strange ramblings that you don't want others to see.
The event that you are refering to was the unfortunate collapse of Fabrice Muamba of Bolton Wanderers during their FA Cup game against Tottenham Hotspurs. Fabrice Muamba is currently recovering from a suspected Heart Attack during the actual game.
It is probably similar to people putting their hands on top of their heads when something fails catastropically, as when a footballer misses a penalty. Chimps do the same. It is probably a bit of (to me) inexplicable and redundant primitive behaviour that we just haven't quite lost.
It is 'blocking' behaviour, a barrier is put up between the the person and whatever is occurring that they don't like - but either they want to keep on watching, or it is not appropriate to cover the eyes.
People do cover/shut their eyes to block but usually when it is not a visual occurrence that they have abad reaction to, just watch passengers when an announcement comes over the tannoy that a plane is delayed - lots of eye blocking and shutting goes on.