It's a nice story. I first heard it about a mad Chinese emperor who wanted to find the wisest man in the empire by setting a near-impossible challenge, and killing everyone who tried and failed to achieve the required accuracy. That version was no more true than this one. I'm pretty sure that Snopes has an article on it, but I don't seem to be able to get there at the moment.
And they even get Niels Bohr's name wrong.