Actually, you are incorrect. There are court cases saying you have to present ID if demanded by a cop.
The cop was responding to a possible house break in. He had to "cross the threshold" to verify this, and he had to verify the person he was talking to was the actual owner. If they believe that a crime is/has occured, there are lower thresholds to entering a possible crime scene. Their job, at that point, is to verify that a crime hasn't occured, and hold anyone who may have committed the crime.
It wasn't an anonymous tip. The woman who made the call has been harassed and ridiculed for the call. I don't see how that's an anonymous tip.
I'll throw in that the professor shouldn't have started by showing the cop his college ID. That doesn't verify that you live at the house, and not everyone knows all the professors at a school.