The OP's premise is that it's one in ten million EACH time, but about one in ten thousand that you will be in a plane crash once in your lifetime if you fly 1,000 times. As I said in a previous post, even though each trial is independent, the cumulative probability is relevant if you are looking at the likelihood of being in a plane crash over a lifetime.

Just like the calculation that if there is a lottery whose odds of winning are one in ten million, then someone who buys one ticket per week for 20 years (i.e., 1,000 trials) faces about a one-in-ten-thousand probability of winning the lottery at least once in his life.

I always found it fascinating that the limit of infinite-trials-of-infinitesimally-small-probability-events -- or the limit of the probability of at least one success over N trials, with probability of success in each individual trial of 1/N, as N approaches infinity, is about 63%, or one minus the inverse of the natural exponent e.