Are you really obligated to provide ID to a cop just because you crossed a campus street? What if you don't have your ID with you?
I'm not sure about the law system in the US, but I know that in the Netherlands it's a requirement to keep some form of ID on you at all times, and when the police asks for it, you have to be able to produce it.
They're quite lenient in practice however, and will generally check with an operator instead if you don't have ID on you. If you do have ID on you and you refuse to produce it however, they can arrest you. Additionally, if you give the wrong name when they're contacting the operator, you can get a fine of $500,-
I don't really see a problem with it. If you break the law, and police approach you about it, they should be able to identify you. Or what if something happens to you, say you're dead in a ditch, and you don't have anything on you to identify you? Considering they're generally not just allowed to open your cellphone due to privacy laws, I can certainly understand the reasoning behind it.
As for this particular instance.. Police was too aggressive and the woman should not have broken the law, and should certainly not have refused to show her identification. If you're accused of something, just do the things they ask, and calmly explain why you feel their accusations are wrong. Her behavior and that of the officers just rubbed off on each other.