Not entirely true. The exception for a local or state police officer to carry in a post office or on any federal property is limited to "official business". See 18USC930.
If he's only going in on a break or off duty to check a PO Box, buy stamps, mail something, or other personal business, he's breaking the law.
(d) Subsection (a) shall not apply to--
(1) the lawful performance of official duties by an officer,
agent, or employee of the United States, a State, or a political
subdivision thereof, who is authorized by law to engage in or
supervise the prevention, detection, investigation, or prosecution
of any violation of law;