There was a shooting at a community college a few years ago in Oregon. Two detectives heard the call and were close by and raced to the school. In the interview the guys were saying how they were praying, and planning. Stop the car, get the vests out of the trunk, put them on, grab their rifles in the trunk, assess the situation, etc.
Well - they pull up and they hear the gunshots from a building. They jump out and race towards the shots with their pistols - the gunman stops shooting and runs into a room and either shoots himself or someone else shot him. (Their was an adult student that retrieved his gun from his car and also went after the gunman - I don’t recall how it ended.)
BUT - the arrival of the detectives, in their suit coats - and racing to engage the shooter is what stopped him. And I believe you are right - they didn’t follow the “plan” that they were probably supposed to wait for backup.
Those two rapidly accessed the situation which may only take a few to several seconds. They likely accessed they were dealing with a lone gunman (usually the case) who didn’t know that they were coming in or from what direction with such rapidity so surprise was on their side.
Yes...that was the school where the “student council” decided there would be no guns on campus