Earlier quoted context omitted.
This to me seems to be the big difference between US policing and what we're used to in e.g. most European countries: A focus on quick resolution at all cost rather than peaceful resolution. UK police for example tends to respond with overwhelming force, clear the area if possible, and contain their potential adversary, and if possible often wait the situation out. They will use violence if they have to, but it ends…
"n unarmed man was shot because police worried he might be a terrorist a few years back" That was 2005, 3 weeks after a successful terrorist attack on the tube, and 1 day after an unsuccessful one. It was news for weeks and resulted in a criminal prosecution for the head of the police force involved.
More broadly, the whole episode made them look incredibly incompetent, callous and uncaring. No action was taken against the officers who were clearly culpable through their abject incompetence (for example, if he was a potential suicide bomber, why wasn't he stopped before he got on a train?). Furthermore, the force took far too long to apologise and admit errors publicly. And they never adequately explained the tactics that led to an innocent man being shot without warning.
This is very similar in character to the issues which plague policing in the USA and has served to sow a great deal of distrust of the police here. Witness the "London riots" in 2011, for example.
And that's also set against a background where they have been publicly found to be "institutionally racist". Subsequently to the de Menezes incident, armed police also "accidentally" shot an unarmed suspect in the shoulder while running upstairs in a house in the Forest Gate raid (which again, just makes them look like amateurs).
And so on.
So our police are very far from perfect - it's just that being better than some of the worst excesses seen in the liberal world is not a hard standard to meet.