What does the vinegar do?
The vinegar lowers the pH in the egg, which makes them easier to peel.
Commercial growers actually adjust their chicken feed to make the eggs' pH lower; one of the reason farm fresh eggs are so hard to peel is that their pH tends to be far higher.
Adding the vinegar is a way to lower the pH after the fact, but of course any acid would work. If you object to vinegar, something like lime juice works the same way.
Man, I need to quit listening to cooking programs............
