Is another myth busted?

Talking about mortality rates, probability of dying and suchlike in elementary vital statistics classes, I used to display my erudition by illustrating odds against dying with the story of Aeschylus, the great Greek tragedian. The story I've told for years is that he was killed by a tortoise that was dropped on his bald head by a passing eagle that mistook his bald head for a rock that would break the tortoise's shell so the eagle could eat its innards. The tortoise, and Aeschylus, both died in the incident according to the story, said to have been witnessed by friends, perhaps seeking the autograph of the author of The Oresteia and many other great tragic plays, only a few of which have survived to our time. Alas, according to Simon Critchley, author of The Book of Dead Philosophers, the story is a myth. Critchley's book is fascinating and fun, but I'm quite put off by this piece of myth-busting. I want the story of how Aeschylus died to be true! It doesn't matter to me as a teacher - I won't be teaching elementary vital statistics again any time soon. But it's such a nice story, I hope Critchley is wrong.