Nobody busted down the doors here; in fact, in no US swatting fatality have the police ever busted doors down.
"First do no harm" is not a universal norm. It applies to medicine because so much of what happens in medicine is in some sense elective; there is an option not to intervene. No such option exists in distress call situations.
I don't think axiomatic reasoning is going to solve the problem of swatting. It's also noteworthy that, even in this case, it wasn't just the police who were tricked into intervening; the swatters got a strange man to break into the victim's house by spoofing messages on Grindr.
Certainly there have both been cases were US police busted doors in response to swatting, e.g. [1] and killed someone in response to swatting, e.g. [2]. Admittedly I'm not sure if they ever happened simultaneously, nor do I think that's relevant to any of the points I have made. The points I made were
- People have been killed while attempting to comply with police orders, which incidentally [2] is an example of (as well as an example of swatting).
- Busting doors during actual hostage situations would get people killed, not swatting. [3] is a particularly powerful example of that...
[1] https://www.youtube.com/watch?v=OVkQ-yheOEE
[2] https://www.nbcnews.com/news/us-news/wichita-officer-who-kil...
[3] https://www.washingtonexaminer.com/news/video-four-dead-in-p...
First that shouldn't be considered probable cause without some supporting evidence, especially given the well established practice of swatting. Supporting evidence here might be as simple as proof (beyond what swatters could spoof) that the call came from the house they're busting down the door of... or peaking in the window. If the police can't establish that a crime is probably happening, they shouldn't be busting down doors, even if that means that they are possible failing to prevent a crime.
Second, busting down the door in response to a hostage situation isn't even a reasonable response, that's just asking for the hostage to be killed... the appropriate response there is to establish what is actually going on, and only then consider violent action, but almost always to try and talk the hostage taker out... in your typical hostage situation the hostage takers want something and the police have all the time in the world, unlike the hostage takers the police can take shifts and get sleep.
Think of this along the lines of the doctors "first, do no harm" principle but applied to rescuing hostages.
The police in sweden this morning freed a hostage this morning at the cost of 20 pizzas, and while I haven't seen how discussed publicly got the other hostage free and the two criminals (back) in custody. Talking really does work...
PS: While I'm at it, can I recommend "never split the difference" as a good book on negotiation, with a side of hostage negotiation stories.