Implying first responders are thugs irks me too, I'm unsure if you've considered the true proportion of cases they respond to that are time sensitive (during which, information parity is low). You could, of course, assert that this means they ought to not respond in the first place - but I think you would find there are a wide range of scenarios that strictly require a rapid and forceful response due to the potential for many victims to be involved (bolstered by gun ownership) with little time to actually validate the circumstances without incurring casualties.
Accidents are unacceptable but our world is complicated and sometimes requires we meet lack of information with immediate action. That is not to say accidents are permissible, but the men putting their lives in harms way to respond to these incidents don't actually know what's occurring either.
You seem to be fairly opinionated about what the system should or should not do, what have you personally done to help improve the conversion ratio between false calls and accidents? I understand this is theoretically ad hominem but I'm personally using it as a heuristic as to the likelihood that your perspective is a luxury belief. We agree that close calls should not be that close, but it's not very different from shaking your fist at the sky unless you actually happen to work in this space (in which case I'm actually very interested in hearing your thoughts). I don't mean to be rude, I'm just being blunt because I believe you're washing over some extremely difficult problems and have little to bring to the table - which is by definition unproductive.