It is sound advice and it is difficult if you're friends with people where you had an easy camaraderie before the promotion.

I have had this bite me a couple of times with people for whom I felt I knew really well and was really comfortable with joking about pretty much anything. Only to find out later that the joke was anything but.

The hard and fast rule has to be both don't joke about firing and don't talk to someone else's direct reports about the performance of their manager.