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: 
For a random signal noise source, you may want noisier resistors that tend to come with larger tolerances because of different technology. Admittedly that's extra-handwavy because the additional noisiness of, say, carbon resistors comes from shot noise while a good random signal noise source would rather tend to rely on Johnson noise (which is more dependable).

Another handwavy reason might be that more precise resistors tend to be trimmed, and bein suitable for trimming implies an underlying structure that is more susceptible to stray inductivity.

Note that either of those reasons is really grasping at straws as an intellectual game.

The straightforward answer is "no", really.
Customers don't know everything, I once returned a suitable product as unsuitable just because I don't know any better.

However customers are always right (tm)

With beer 5% is better than 1%, perhaps your customer was thinking along those lines.