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I've heard of this kind of thing before, but always just thought it was silly - sure if you sample random observations over the lifetime of a thing, the median will be right in the middle, but that's a tautology, it's by definition. And it doesn't have any predictive power because the observations at the beginning or end have an equal probability to the ones in the middle, there's no way for any of them to know where they were until after the fact.
Using this method, this company that went under in 2006 would have guessed in the year 2000 that they would last another 1400 years. While Nintendo in 1900 would have guessed only another 11 years.