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: 
If *everything* else is the same then there is no technical reason to prefer a looser tolerance, so I think you are correct.

Of course there are situations where a particular manufacturer and part number may be required for regulatory or other similar reasons and no substitutes are permissible. And there are many resistor characteristics that are important in some situations but are not specified by the nominal resistance value + tolerance + power rating (or package). For example, a composition resistor may be specified because of superior power pulse handling, but they cannot be made in tight tolerances due to the way they are manufactured. A 1% film resistor of the same value, package size and power dissipation rating might fail in short order.
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).