Journalists certainly shouldn't have more rights than the rest of the citizenry. On the other hand, in the US and some other places, they do have an almost sacred responsibility to report to the world what they see and that ought to grant them access to things it would be impractical for all the rest of us to view on our own. They are supposed to be our eyes and ears.
In any case, the Times does have a significant legal department and expensive outside counsel as well as a commitment to protecting that sacred trust with public (see some of Bill Keller's recent writings, for example, on the potential chilling effect on proposed legislation to tamp down "leaks" by officials). Also, the Times has an above average track record in litigating major First Amendment cases (the Pentagon Papers case being a prime example).
So, while it's certainly not a matter of the Times having more rights, but that it other other journalistic enterprises, investigating and reporting on behalf of the public, ought to have bigger mouths filled with more teeth. Robert Stolarik doesn't and should not have more rights than our own Helen Hill; but he sure does have, through his employer, a lot more ability to fight back. If the Times wins, we all win.
I don't have a problem with the notion that a man or woman with a press pass ought to be able to access places I can't personally access. In fact, I think it's critical (picture all 300 million of us standing backstage at the upcoming political conventions; actually, maybe that's not such a bad idea). That said, I don't want to be arrested for taking a picture on the subway.
As for asking for a badge number, doesn't the officer have to put that on the summons or other paperwork? Isn't that also part of the transparency we all ought to expect? I can't imagine that they could hide that from someone they arrest; it is part of the public record after all.
Journalists shouldn't prevent the police from doing their jobs, but the equation ought to be reciprocal. While I can imagine a situation where a cop could rightly say to photographer, "you need to step away so I can do my job and protect public safety," this doesn't seem like a scenario where that was necessary.
Bottom line for me is that I would not want to live in a society that lacked either a professional police force or professional journalists (emphasis on professionalism in both cases). When the balance between them gets out of kilter, trouble usually ensues. Just my two cents.