The truth is it matters a lot more than we think. People are usually skeptical of others they do business with for the first time. There's an assumption that the service provider isn't giving all the facts and there's something they don't know that's going to cost them more money.
How do you solve that problem? Simple, by keeping a list of as many people you've ever done business with as you can then give the customer the names and numbers of those people, without them having to ask, and let them know that they can call as many or as few of those customers as they want because not only are you confident that your previous customers would vouch for your work but they'll also vouch for your integrity.