Here's the *real* bottom line: you are always required to cooperate, regardless of whether the police are right or wrong.
Even if the police are dead wrong, and you know that they are dead wrong (hint: you never really know at the time), you are required to cooperate.
Do I like that? Not really. But, that's what the law is - you have to cooperate.* What we've said, as a society, is that we'd rather have these things sorted out in a courtroom, rather than on the side of the road.
Now, in an idea world, if you tell a cop "no, I don't want to talk to you," then he/she is going to say "OK," unless there is some kind of RS or PC to detain you. In the real world, though, we never truly know what will happen; you also never know either: 1) if I'm actually right; 2) if a police officer will know that I'm right; 3) if a judge will agree that I'm actually right; or 3) if your case will be the appellate case that completely changes things, either for or against your benefit.
So, my advice: assert your rights. But don't resist unless you're willing to assume the risks that come with it.
* There are certain exceptions to this. For purposes of posting on a public forum, though, I'm going to tell you that there is always a duty to peacefully cooperate.