I believe law enforcement is allowed to say anything they want to. As a civilian, you're not allowed to lie to most LEOs; but they're allowed to lie to you.
They also can't lie about the legality of actions while in the visible position of being the police. That means they CAN lie about it when undercover.
(I have a lot of respect for the police: they accept a lot of risk to try to ensure a civil society in exchange for not a lot of reward, but there's little doubt that if they see themselves in an adversarial relationship with someone they are willing and able to mislead or misdirect that person in order to accomplish their aims. There is a reason that the Miranda Warning became a legal requirement.)