This line: "You do not need to provide any personally identifying information in order to use Chrome" is intended to cover pretty much all of the cases you describe. I'm not going to speculate on legal issues.
I read that line a very different way and on its face it does mean something very different. The (very good) lawyers at Google may want to look at how this is phrased if it is intended to mean more than what it says plainly.
No need to speculate as appellate courts (and Google's own recent trials) have made the law quite clear.
