This was one of the more lengthy lessons I had to learn when I started out. I'm in a very small town, and I knew many of my clients as friends before they were my clients. So I got a lot of, "Hey, what does this mean...?" calls. After one particularly frustrating day of looking at the books, I decided that had to stop. My favorite line was similar to yours, "It could be a lot of things, I would have to put it on my bench to sort it out. I've got a couple of customers ahead of you but I could probably get it back you in a day. You want me to come grab that today?"
Telling them they were in line with other customers made it clear that they were customers too. At that point the wheat separated from the chaff fairly quickly. Not that any of my friends who decided not to pay didn't remain my friends, but they know that I am running a business and only come to me when they really need something and are ready to pay. To be honest, the butterflies were entirely in my own stomach, and none of my friends/customers had any issue paying or deciding not to call. It was actually pretty pain free and simple.