Nowhere in this country is a citizen required to carry or produce ID in public. Furthermore, officers need reasonable suspicion that you have committed, or are about to commit, a crime before you are required to identify yourself. You are never required to explain your actions.
It depends on your definition of fine, but probably, yes.
If 'fine' means not hassled or delayed in any way, then it already didn't work out 'fine'. If you're willing to add on another hour or two waiting, perhaps the night, waiting at the police station as 'fine', then you're still good.
I'm not sure if you're concerned that you would have been beaten or harmed? I'm sure it's not out of the question, it never is, but so long as you remained peacable as you explained it to the officer, I'm guessing it wasn't likely.
Every district / cop / municipality is of course different though.
It's semi-free for you to file a civil suit against the arresting officer for wrongful imprisonment as well.
I'm not saying it wouldn't be inconvenient, but fear of inconvenience isn't necessarily a great reason to lay down your civil rights.
That said, I don't mean to imply any judgement, I'm just curious as to "what would have happened". I've been in a number of scenarios similar to this one and have never been beaten, attacked, or in court spending a great deal to defend myself. Not to say it couldn't easily have happened, every encounter is different.
I don't know whether to agree with your second sentence or not. It looks like reasonable suspicion is required, but it also sounds like individual states' stop-and-identify laws are varied and vague.
