there are times when other factors can overrule that, IMO.
Of course. Our actions as firefighters are defined by operating guidelines. Each guideline, includes a reference to the possible need to do something else. But, if you, as a firefighter singularly decide to do something which contradicts a guideline, you will probably called upon to explain later, particularly if something goes wrong. If you're operating within the guideline, and something goes wrong, it's pretty well an automatic "well, you did your best". If you were outside the guideline, people are going to ask and think a lot before they may reach the same conclusion.
We move patients as little as possible, but sometimes you have to move them. If you have to move them, you control their condition and position as much as you can before you move them. But, if there's a critical need to move them, you do what you have to do, with the foregoing considered. So If I have to suddenly drag someone out of immediate peril, it is what it is, I may not make their condition worse, while I'll probably save their life. But, to move someone, possibly loose inside a vehicle, by pulling the vehicle, means that they could flop around inside the vehicle as it moves (or rolls over), and become more badly injured. The vehicle could catch fire while being moved, and then you just trapped them inside,
and caused a fire! Or, the vehicle could further jam, so when moved, is less accessible for extrication. We've taken as long as 45 minutes to cut someone from a car without inuring them further.
Upon arrival, the first thing you do before patient assessment and assistance is to assess the scene, which these police obviously did well - patient safety and condition, bystander safety, and your safety. Correctly done (and hopefully called in), that assessment forms the basis of what you'll do next, and how urgently. If the patient is injured, it is never not urgent, you have an hour. But, particularly with medics arriving on scene, if you have the time, you should use some of the time to do it right, assess and immobilize the patient, then move them.
During auto extrication training I conducted, I had an old 172 fuselage taken to the wrecking yard too. While I was teaching to look for airbags before cutting through a B post, I was teaching that's where the fuel lines are in a Cessna!
Experience comes from both doing it a lot, but also realizing how close your success was to non success in many ways, and remembering that for next time!