Right or wrong, the law allows them to do it. If you lie to police in the course of their investigation, you can be charged with a Class A misdemeanor in NY. Obstruction of Governmental Administration I believe they call it. There's a similar Federal law. Even if you believe something to be true, and it turns out it isn't, you can still be charged. So, never lie to the police, and always be very careful what you say to them.