You must realise that's as statistically complete as those who give first or second hand stories of injuries but they were dismissed. There could have been a hundred children killed a week on bikes but you wouldn't have known any of them in a country of 15 million children. There weren't of course, and that's a very good thing.
The point is that you're gambling - you've said yourself you're weighing up the odds. You of course do things to increase the odds in your favour (teaching good road craft, keeping their bikes maintained well etc).
The issue for me is personally is that the consequences can be so catastrophic that it's worth doing what you can to mitigate the effects if it does occur. I still do the things you do, but stick a lid on their bonce too.
The likelihood of eight lift cables snapping is very low but there is still an additional safety brake as the consequences are so catastrophic - it's the same deal for me.