Actually I don't believe that everyone is 'into fairness'. Far from it.
I may be old and jaded, but I see repeated examples of people who are more into 'getting theirs' than they are into being 'fair' - each and every day.
To your point of 'perception of fairness', I agree with you that this is the nexus of most any conflict - one side thinks they are being more fair than the other.
And I am not immune either - we all do things to benefit ourselves and our loved ones... and sometimes these things are to the detriment (or at the expense) of others and/or their loved ones. You are right about how we each perceive what is fair and what isn't - we all possess our own biases.
IMO, what is 'fair' is better judged by many than by any individual.
So back to the case at hand...
Because LE has been granted the ability/option to take an individuals liberty (or life), the public's 'perception of fairness' will always be magnified and somewhat distorted.
This burden worn by LE - because of their position of power - is what it is. Is it 'fair' to LE? Probably not. But that doesn't make it any less real, IMO.
And LE are humans just like the rest of us... they will all have good and bad days just like the rest of us.
Now, the 'rest of us' can have bad days, snap at the spouse, kick our dogs (metaphorically) and generally be nasty to others as a result of our bad days. The thing is, LE can't exhibit these types of things when they have their bad days - or they end up on YouTube and CNN.
Is that fair? Not hardly. But it is part of the burden you accept when you carry the badge and strap on your gun. You are, and should be, judged to a higher standard because of this.
LE has to be MORE fair and LESS provocative than the average citizens they have to deal with. And that shit aint fair.