New Arizona law: "I'll go vacation somewhere the police won't stop me in the street to ask me to prove my citizenship."

Whether or not it is actually accurate, this discussion of the new Arizona law would sound some alarm to anyone considering traveling to Arizona. As a non-US citizen in the US, I'd usually carry my drivers license but not necessarily my Green Card everywhere, as I don't want to misplace my Green Card. Would I have to carry my Green Card around when I am in Arizona? It sounds like I would have to. A drivers license alone doesn't necessarily prove someone is in the US legally. That's an extra pain for me, so given choice, I would take my business travel elsewhere. It's also a pain for tourists who seemingly would have to carry their passports around all the time, which increases the risk of them being lost or stolen.