"...the First Amendment protects the right to record [police/gov't officials carrying out their duties in public places] regardless of whether the police/officials consent. This constitutional right would override any state or federal laws that would otherwise prohibit such recording."
You're thinking of the rules regarding phone conversations (one party vs. two party states). You're allowed to record your interactions with police, although sometimes they'll lie and tell you you aren't.
Two-party consent laws do not just apply to telephone calls. In California, Cal. Penal Code § 632 applies to "confidential communication".
Sure, but being arrested by the cops isn't confidential communication.
See Glik v. Cunniffe; you can record the police in public spaces, and laws that state otherwise are unconstitutional.
It doesn't seem like that's entirely settled yet since the ACLUM is still battling it out in court according to:
My reading of that article is that what's currently being fought over is the secrecy of the recoring activity, rather than consent. That it is this level of nuance that is being argued in court suggests that the issue of consent is well seettled.