It's extremely likely in the computer/PC world that your first inclination doesn't fix the problem. Sometimes rebooting DOES fix the problem, and sometimes it doesn't. What then? Another $10,000 for the next attempt?
Clearly, if he KNEW that turning the one screw would fix the problem, it's a different case altogether, but I'm suggesting that it's rarely that cut and dry.
I've never in all my years had this problem. There never was something I couldn't fix, but there were plenty of things that took more time than I initially thought. I usually tell the client "it seems that I won't be able to complete the task in the time of the original estimation, do you want me to stop now and you don't have to pay, or do you want me to try for an extra 1-2 hours and get it fixed?"
People always seem to pick the latter, and I haven't had any unresolved problems or unsatisfied customers yet....