I have heard of a wide range of stories where people were saved using some string, a piece of flint etc. (A related example from earlier this month is reported in the Hamilton Advertiser where a boy used the laces from his trousers to save a dog.)
and if they had had a survival kit they would have used that, but the problem is that most people do not carry a survival kit. The only people who regularly do tend to be military, and their kits do get used - records are available on 2nd World War aircrew who had to bail out over enemy lands, or more recently Andy McNab described using some of his emergency kit in the middle east in Bravo Two-Zero.
Some paracord was even used by astronauts during STS-82, the second Space Shuttle mission to repair the Hubble Space Telescope!
More anecdotally, my father once had to use paracord to tie Prusik knots to get up out of a crevasse (not sure whether it was Antarctica or Greenland) - not a full emergency, as the rest of the team had possible alternatives, but a good practical use, nonetheless.