No. The poster is claiming that a cop can go into any public space because he is a cop. The mayor's office is a public space. Therefore, under the poster's guidelines, a cop should be able to go into the mayors office after hours and search it at will if he disagrees with the mayor's politics.
The fact that the cop was out of his jurisdiction just makes the poster's claim even more absurd. This would be like a cop from Camden driving over to Philly during his shift and searching John Street's locked office...