Your papers.....are not in order....
Let’s assume the cop was going to write her a ticket for jaywalking. First rule, never argue with the cop at the scene. Take the ticket and fight it in court. There’s a good chance the cop won’t show and it will be dismissed, or that the judge will accept your explanation and drop it. OTOH, if you piss the cop off, he will remember you, make sure to show up, and possibly lie about what happened. But if you don’t show your ID, the cop can’t just issue you a citation, because you could be giving him a fake name. So he either has to back down completely, or detain you.