Every PM is sent at a specific time. As she sends every member of the populace's PM at the same time (indicated by"undisclosed recipients" in the message header), and none of the participants with special roles received any PMs at this specific time (to the second), only the populace should be able to tell me the correct timestamp.
But this is an exploit and should be regarded as cheating, in my opinion. I shouldn't even have brought it up.