OP is missing some information. The primary concern was that the cops were complaining over the guy's car playing loud music, not just recording police.
Now, to be honest, everyone was kind of being an asshole here. Well, everyone but the dog. Clearly not aggressive and was an unfortunate victim in everything.
The owner: Shut off your bloody music. If there's a tight police situation going on nearby (so at least expect a cop might get grouchy), turn off your fucking music so they can do their work. That's the first thing you should do when you notice something's happening. Second, I know that keeping a dog in a car in a summer's day isn't a good idea typically, but at least tie the dog to a seat. A flex-leash isn't that great, but it'll be better than just putting the dog in a car with an easy way to get out.
The cops: This seemed to escalate far higher than it should've. The owner didn't help, but it's their reputation on the line. No one likes it when animals are involved. The cops should've given him the time to properly restrain his dog, or maybe even give him some ideas.. Also going to mention that cops in general are CRAP with reading animal behaviour. If you're perceived to be a threat by the dog (or at least a concern), then slow down and think. Reaching for the leash is NOT the correct way to handle it, especially if a dude is pointing a gun at the dog from the moment it comes out and tension is high. Let the man get his dog and properly restrain it. Animal behaviour is not really part of their education, which is why fuck-ups like this happen and they do a number to their PR. Some cops do tasers and pepper spray, and while I agree that a gun stops an angry dog more reliably, they are an option.
There are a lot of bad cases of police being shitty with animals (some of them more black and white with the cops at fault). Dogs have been shot for barking at cops yet being properly contained and not a threat. Last year there was a case of a cop breaking into the wrong house, not allowing the owners to restrain their dog, and the dog was shot dead. A cop pulled up to a lady's house (not for an investigation. I think it was to ask for directions) and a dog ran up only to be immediately shot when the cop was just outside his car. In that case, apparently the cop also tried to bribe the lady for the security camera footage. A few years ago, a K9 unit was using people's yards for practice without any notification. A man's dog was in his yard, attacked the police dog when they came in, and the cop shot the guy's dog (nothing wrong with protecting the police dog, but the fact remains that this was entirely the fault of the cops for not letting residents know).
And some more recent ones.
Less than two months ago [http://www.suntimes.com/news/metro/20198854-418/stories-differ-over-pitbull-shot-by-off-duty-chicago-cop.html], an off-duty cop shot a 4 month old puppy that ran out of the yard near the officer's child (puppy apparently wasn't a threat). Stories here aren't clear, but considering the excuse for the shooting was "pitbulls eat kids" and ignoring the fact that this was noticeably a PUPPY doing PUPPY things, it was a serious judgement error.
Just recently [http://fox8.com/2013/06/11/police-defend-shooting-of-feral-cats-outside-home/] there's also a case of a woman wanting stray kittens to be brought off her property, and while she had a feeling they were going to be put down, the humane officer that was sent shot all of them on the lady's own property. Technically a form of euthanasia, but didn't anyone think "hey, this might turn out badly"?
So ya, cops need to clean up their image, staff, and protocol on how to handle animals.