This is distinctly not a "Performance Management Plan", as the plan involves the employee and provides clear guidelines for success. If you're concealing that they're on a PIP at all, it's not a PIP, it's literally just the declaration that you intend to fire someone you deem low performing.
edit And I'll add, I don't think they're legally obligated to tell a person they're not performing to their desired standard, as at-will employment, but it just seems silly to call something a PIP that is actually not at all a PIP.