There is no functionality for that to happen. New message notifications are always sent to the recipient user and am unable to confirm such an issue; it also appears literally impossible in code review. Only reason that could happen is if they replied to the email notification, which they of course shouldn't, or some sort of server configuration replicating the emails, but you'd see that for registration emails as well. PMS notifications can be turned off within Private Message System > Parameters > Internal > Notification.