Clean Install Addresses Symptoms, but not cause
A clean re-install and data restore will revitalize the PC to it's original glory. But, the cause of the problem might be hiding in the backed up files. Or, most end users will later do the same thing that caused the original problem.
A competent technician should let the customer know their options; backup and re-install or hunt down the culprit and fix it (with the caveat that the final solution might be to do a re-install anyway).
If you hunt down and find the cause of the problem, the end user can be aware of what NOT to do next time. Hunting down the cause might prevent the problem from rearing its ugly head again.
In either case, be honest with yourself and the customer. Also, be aware of your environment. In a corporate environment, speed is of the essence. Unless otherwise specified in some SOP manual, time spent hunting down the cause shouldn't exceed the time required to do a re-install/restore.