I have fired an employee for stealing lunches (with plenty of evidence, of course). I would have fired the person in this story immediately if it were within my power.
Similarly, I have also fired people for other obvious character failures, such lying about bereavement leave to take time off. (It happened so often at one job that I ceased to be amazed when I caught it.) For example, one guy brought me an obituary for his dad that was obviously altered (fonts on dates didn't match, etc.). Google immediately informed me that his dad had died three years earlier. That was a fun conversation.
For those who think such behavior should be considered a mere mistake and that firing is too extreme, please tell me how such poor character can be corrected by actions taken by management at their workplace. If the job requires good character, then the only correct response to such behavior is to separate them from the company, as happened in this case.