The "... couldn't seem to find any record ..." looks weak to me. If I was a customer I would think you are pretending you can't find the record. Either you can find the record or you can't, so say something like "We have no record of a computer with that problem".
I can see that, but I don't think it looks like weakness so much as an unwillingness to publicly assert the client is absolutely wrong. It's the difference between "I think you've made a mistake" and "You have no idea what you're talking about." I guess this comes from my background; I was taught to try showing the customer that he's wrong before telling him he's wrong (granted, this isn't a real customer, but the outside world doesn't know that).