Your error is in thinking they "thwart" the crime. They don't. They punish after the fact. That's still upholding the law(punishment for breaking it) without protecting a person. There is no law that says they have to put their lives in danger, so they're not breaking any laws when they don't intervene.
It's not mental gymnastics. It's that laws are specific so as not to be too broad and overreaching and in this case, there is a massive Blindspot that has not only been allowed to exist, but has been further codified in legal precedent.
"Protect and serve" is a PR statement. It is not a codified law anywhere.