Correct -- there is no legal requirement in any state to carry identification papers. Indeed, there's no legal requirement to own official identification papers of any kind.

But you may, in certain circumstances, be required to identify yourself to the satisfaction of the police.

If you do not have official ID, or if they suspect your ID has been forged or altered, they can detain you to verify your identity. If your local police have good mobile I.T. and you have an ID that you simply aren't carrying, they can run your identifying information and pull your picture. If they aren't quite that well-equipped, they can at least call in your information by radio and see if it matches a known ID. There are a number of databases that could be used, including driver licensing, court records, ICE databases if they suspect you're not in the country legally, etc.

Of course, the police have some discretion on when they're satisfied with your identity, and their discretion may be influenced by your attitude. It's perfectly legal not to have ID on your person, but if they ask you to identify yourself, either give them your ID or give them the information they need. If you think it's an unjustified stop, you're generally better off filing a complaint later than arguing with an officer along side the road.