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).
Of course agreeing with all other answers that generally say "no", I see those four cases:

1. In analog musical circuits not-tight values may produce "the tone", when all loose tolerances in filters and other elements sum up, making one's tone less reproducable. Thus, even when you build a clone of your sound processor and give it to a friend, you two sound slightly differently. Though this does not apply to Hi-Fi equipment - rather artistic ones (e.g. guitar effects, synthesizers etc.).
2. It was the point to measure them and prepare some report/statistics - for example for students classes.
3. Preparation for bigger order: as 5%s are cheaper, he searched for best under that price label.
4. Thinking about next serviceman: seeing 1% would think "why it is so tight and do I really need the same for replacement?".
About half a year ago I had to replace 1200 uF capacitor in somehow regular switching power supply. As a hobbyist I was wondering for a while if I really need this value (I had only 1000 uFs in my box and live in a place without electronic store by the corner). I had used 1000 uF I had and since then owner of the equipment hasn't complained - and we are still friends! ;D.

The customer may have not mentioned that being sure that you will provide him with 5%s as defaults.