"Last week when I told an employee his name was pulled for a random test, he said he took his wife's prescription pain medication the night before for a backache. We sent him for the test, but was that even necessary since he confessed?"
Following through on the random drug test was a good idea, especially if the test was required by an authority (e.g., DOT, Ohio Bureau of Workers' Compensation' Drug-Free Safety Program). It also helps maintain consistency with your random testing process.
Now to address the confession ...