There is, honestly, less of a reason to believe it's false. They may be lying but our legal system relies on us trusting the police to be honest and, ideally, strongly punishes those who abuse that trust.
I'm happy to concede that policing in America has long eroded that trust but it's still a requirement that you obey and openly communicate with anyone identifying themselves as law enforcement.
Actually yea - I was wrongish on this one. It's a state level decision[1] with different requirements and generally a requirement of suspicion of guilt. I was mostly thinking of surface level information (identification and the like) rather than any sort of detailed information that might contribute to guilt - but even that surface level information is still protected information.
I'm happy to concede that policing in America has long eroded that trust but it's still a requirement that you obey and openly communicate with anyone identifying themselves as law enforcement.