IOW, if I see you standing on the street, minding your own business, I can probably get you arrested by saying "There's a guy over here that is bothering my family. I think he looks like trouble." Especially now that I know you'll refuse to show your ID.
When the cops come, they will probably talk quietly to you, and ask for your ID so they can run a quick check for warrants, etc. If you repeated refuse and say "Eff you, I know my rights", they will probably take you in until they determine who you are and whether you are, indeed, a troublemaker.
Is it right? NO, but it's not the cops fault. Whoever called it in put the "trouble" into the complaint. The cops are just reacting to what they've been told.