While there are cases where privacy rights should kick in (your example of private phone calls is a good one), I cannot imagine how an on-duty and in uniform officer doing something in public (where there is no reasonable expectation of privacy) should expect to not be recorded. That officer is armed and dangerous. In some circumstances, is legally allowed to use deadly force against citizens. Abuse of that power has happened to frequently to claim that the officer needs privacy to carry out their public service.