The other common charge is the "impeding an investigation" deal. There is some validity to this when someone gets right into the middle of an arrest or incident investigation with their camera. Police should have (IMO) the ability to detain someone who is interfering with the process, but it should done with discretion.
And I think that's the crux of the problem. Lack of judgment and discretion. All around. Part of this is fueled by the chicken vs. egg syndrome. Cops feel put upon by the public. They choose to limit liability by limiting recording. Conversely, the public feels that the police are increasingly hostile and confrontational with the public. They want to record to protect their rights against police abuse. Who started it? Don't know. Don't care.
I choose to start at a point of presumptive innocence. Even if you're stopped, even if the evidence is compelling, you are presumed innocent. Since it is happening in public and especially since the reasonable presumption is that the police are likely recording you, it is entirely reasonable to expect that you have the right to record as well.
Wiretapping laws assume that one or more parties to the recording are unaware of the recording, but that clearly isn't the case here. What is going on here is the public servant is objecting to being recorded. I don't think that presumption of privacy is correct.