Absent without leave: Can we fire for violating vacation policy?

Q. We recently could not reach an employee who works off-site. Then we learned he was responding to customer messages by saying he was on vacation. After we learned this, he contacted his supervisor and said he had been on vacation and would be on vacation the rest of the week. His supervisor reports that he had not requested vacation time beforehand—and our policy states that vacation time must be preapproved. This employee had been a marginal performer, and now his supervisor wants to fire him. Can we fire him for this? ...