Question: I work at an electronics store and the other day a customer came in who was rebuilding a circuit board. I sold him some resistors, but later he came back in wanting to return some of them because they were only 1% tolerance, and he needed 5%. I'm not an engineer but I have a hobbyist's understanding of electronics, and I was under the impression that there are situations that would call for a more exact value, but never a *less* exact one. Am I mistaken?

Answer: 
There might be a hidden specification in wanting 5% - the circuit might be relying on carbon film (typically 5%, "beige bones") vs metal film (typically 1%, "blue bones") resistors. Carbon film has different behaviour under temporary overloads (in a bad design, a metal film resistor might fail) and looks (which might be relevant if someone is restoring vintage equipment and wants their resistors as beige as they were).
There's no technical benefit. All resistors are ideally 0% tolerance. As they can't be, circuits should be designed for the part's worst value at tolerance. It's a design complication that leads to performance variance.

In the past, 5% resistors have been significantly cheaper than 1% resistors. That becomes important when buying in volume rather than handfuls. Nowadays, 1% resistors are the standard part and there's no cost benefit in 5% resistors.

*My guesses here:*

* Your customer was buying replacement parts for an existing circuit and so wanted like-for-like, not understanding there were no downsides to a 1% part
* Your customer was buying against a spec' or parts list and simply wanted the specified part