Hero, I'll preface my comments that I do give weight to your being a police officer and I consider myself generally a big supporter of police.
Having said that, one general comment - everyone, police and not police, is subject to issues - where police have to follow all kinds of rules and deal with criminals frequently where those rules put them in danger, they can develop a bias of not being fond of some of those rules. It just takes a few cases of the inevitable situation where they know better than the rules, reasonably, to start to erode that.
Conversely, when the public sees the film of police behaving badly, beating someone without justification, shooting someone 100 times without justification, they tend to be more suspicious of all police as a result of the worst few, rather than remembering how few those are.
Then there are institutional pressures - police who rely on each other for their lives and are largely sympathetic to each other not wanting to get each other in trouble, politicians who might not want bad press on something, all kinds of things. Take a policy like stop and frisk - take the same facts, a small percent found with guns, and some will say that's a great success removing hundreds (or thousands?) of guns and saving lives, others a great failure of civil rights and affecting over 90% 'innocent' people. Who's right?
Rachel Maddow reported that the FBI investigates itself in shootings, and in the last 150 investigations, all 150 were found justified. Maybe they were? But what's both more credible and effective in finding they weren't, that or if a more independent group did the investigating?
The argument that an outside force 'doesn't understand' the police is easily solved. There are all kinds of ways to inform the people of the police point of view, such as liaisons and training and experience. Many cities have 'citizen police review boards' that seem to solve a lot of problems nicely despite some opposition from some of the police with those concerns.
There's no perfect system, the independent review likely would have examples of just the thing you're worried about - but would it be better overall? I suspect so.