About 45 years ago, I had a boss who'd give someone a job to do and then later, probably the next day, would ask what they were doing, why they were doing it and who told them to do it. When he was told it was him, he'd deny it.
A colleague of mine, Peter, suggested we keep a record of all such tasks in a book and get the boss to sign against each one as having agreed the description of the task. We told the boss that the purpose was to keep a log of when a task was assigned, completed, etc. and who had ordered it. He was kept in the dark as to the true reason and so agreed it was a good idea.
The day after the first task went in the book and was signed by the boss, he came into our office and asked what we were doing. After we told him, the conversation went something like this:
Boss: "Who told you to do that?"
Peter, opening the book: "You did. Here's where you've signed against the task."
Boss: "THAT'S NOT MY SIGNATURE!"
If e-mails had been around and we'd shown him one he'd sent us, he would have still denied all knowledge of it and hinted that we'd somehow forged it. If he'd been in PHB's position here, he'd have insisted that he had sent an e-mail. If there was no trace of it, he'd have said that it must have been removed from the system.
I once had a boss whose conversations sometimes went like this. Usually we would sit down to discuss a project and he would get a call and have to leave. Days later, he would ask me why I hadn't done such-and-such, which was the topic of the interrupted meeting.