On your first point, the media often leaves out important bits of information or blatantly misrepresents a lot of the actual details of police cases, so the general public only has the knowledge that is given to them. The courts have far more information, which is shared with the jury during the various processes, so a full picture is formed. The reason some of these cases even become news is because it can be spun to fit a specific agenda. The other reason is that they are uncommon, in actuality. There's roughly 1 million le officers in this country, with literally 10's of millions of interactions with the public annually. Most all of us in the profession come to work, do our jobs to the best of our abilities, and try to make a difference. The media pounces on the few that will increase their ratings. I'm also in favor of in-car cameras (they've helped my cases many times), and don't care if my Department eventually transitions over to body cameras. I have nothing to hide while doing my job. Oddly enough, there's a big lobby forming against body cameras because of perceived privacy issues if used in peoples homes.
As to your second point, if you commit a traffic violation in front of me, it doesn't matter at all where you're from. Most times, out-of-staters just get a warning from me instead of a summons. I can't speak to your experience, however.