Hmmm...
Difficult to render an infomed personal judgement because I wasn't there and didn't witness the event...video not withstanding. (Which I haven't watched yet anyway, being at work.)
I should think that the key to handling such an encounter with a police officer is knowing what to say in the first place. As a person who carries concealed, I have run myself through many different scenarios and try to think ahead for any given circumstance. Such as being pulled over for a "safety stop" late July 4th. Or getting gas. Or walking through Walmart.
What one says (and how one says it) has a great impact on how people view them and what actions they may take. Anybody who chooses to hide behind arrogance and a belligerant attitude, even if they're in the right, is setting themselves up for a fall regardless. And, like it or not, the officer with the gun is NOT someone to play stupid, silly games with.
If you carry a gun, playing stupid and silly games shouldn't be on your agenda in the first place.
If I'm questioned by a police officer, one of the things I always consider is I may not know why I'm being questioned. Did the officer get a call about me? From whom and for what reason? Did something else happen in the area that I don't know about? Does my basic description match something/someone he's looking for?
When I'm pulled over for a traffic violation, odds are pretty darned good that I know why. But my basic manners should not be any different.
In any case, my answers and my demeanor should not be engineered to trip any precipitous response from the police officer. I want to come across as polite, clear headed, and reasonable while protecting my own rights.
There are all kinds of ways, and advice, about answering questions an officer asks. But I would say that one should start with the actual questions the officer asks and not go off into tangents. If the question is "what are you doing?" while you're standing in line to pay for gas, then the answer should be something along the line of "Paying for some gas, officer" because THAT'S WHAT YOU'RE DOING! Going off on a tangent about exercising your right to open carry is off topic and very quickly leads the officer into questions about that based on YOUR responses. Make HIM segway into that.
If it's a request to identify yourself, whether simply giving him your name or showing an ID, then answer politely in accordance with whatever local laws are in effect for you. If such a request is bound by law based on a reasonable suspicion of some criminal activity, then politely ask why and what you're suspected of. If you refuse, then do so POLITELY and ONLY in compliance with the law. Your response should ALWAYS be calm and polite, never giving reason to upset or incite. And even so...your technically legal and polite response may STILL cause you problems.
YOU are the one to decide how much to say to the police and how it is said. If you do say something, you had better engage your brain first before you end up eating your own feet as a result.