Well, I partially disagree.
A cop can give you a ticket without clocking you if his judgment tells him you are speeding. He can even estimate how fast you were going. Police are considered expert witnesses in matters of speeding (in court). He can also just charge you with reckless or careless driving without reference to your actual speed.
As far as where he can chase you, under the doctrine of "hot pursuit" he can even follow you into another jurisdiction (e.g., another state) if he has observed you speeding within his jurisdiction and he has followed you out of it before he catches you. Not that I have any personal experience with these things.
