Your point about a large sample size is absolutely true. But just what constitutes a sufficiently large sample size depends upon the probabilities involved. For tossing a fair coin, where the odds are 50:50, a sample size of 1,000 is plenty large enough for the probabilities to emerge from any statistical anomolies. But for a much less likely event, like winning the Power Ball Lottery, where the odds of getting all 5 numbers plus the Power Ball are about 1 in 274 Million, a much, much larger sample size is required. The Power Ball Jackpot has gotten as high as $1.5 Billion, and with a payout of only about 50%, and chances costing $2, that means that more than 1.5 Billion tickets were sold, in the aggregate, over several drawings, before there was a winning combination sold. And in that case, there were 5 winners. In Lotto games, we can calculate the odds precisely because of the nature of the game - pure random number selection. But even a sample size which is about 6 times the calculated odds against (274 million x 6) may be necessary before a positive outcome appears.
With a sample size of 5,000,000 Snuba experiences, all we can say with any confidence is that the odds of an injury are probably (with about a 95% confidence) less than 1:1,000,000. And even with that big a sample size, there is still a non-zero chance (though very, very small) that the odds might be as high as 1:500,000.
