1. The way it usually goes is they don't lie; they just say no when asked to provide ID.
2. It seems like the police officer has to be able to state what crime they suspect has been committed. Standing around looking suspicious is what usually draws attention but it isn't a crime so they just say no when the police ask for ID.
But that's for local police in some states. So again, is it different when you refuse ID to a federal officer? I think the answer is no, that there is no federal statute that requires you to identify yourself to a federal officer unless you are suspected of a committing a crime. But IANAL nor a member of law enforcement nor one of those ornery people who like to challenge the police and even hope they will be arrested on false pretenses so they can have fun suing the police.