that if you don't happen to have your green card on you, you can be tossed in the officer's car and dragged off without being given the opportunity to produce it.

but if you don't happen to have your Driver's ID on you, you'll likely be let off the hook as long as you're in the system (in other words, if the officer can look up your name in his computer). At worst, you'll be written a ticket for a fine and will have only 24 hrs to produce your ID for the court. But I've never once heard of anyone being hauled off for not having their driver's ID.

It'll be hard to produce your green card from inside the local jail, if possible, but the fact is that the person should have a certain amount of time to produce it before being arrested. While there will probably be some officers and courts who do this, a large portion of Arizona cops are rather racist against the Latino population and it probably won't happen that way.