Here is an example where officers adopt the liability at their own risk ... an officer receives a call of a fight in progress - no weapons involved, but it is man beating a woman. The officer is a couple of miles away. It does not fit the requirements per agency policy for a code 3 response with lights and sirens. So, the officer can choose to respond at the speed limit and take, perhaps 6 to 8 minutes to get to the scene, Or, he can push the envelope, exceed the limit, and maybe even make a screwy turn or two and get there in half that time.
Considering a LONG fight lasts for four minutes, the odds are better that the officer can get there in time to save a person from greater harm if he or she pushes the envelope. If the officer gets into a collision, he or she will adopt liability for the accident.
Is it worth the risk? Well, if it was you or your loved one on the receiving end of such a beating, would you prefer the cops get there ASAP or would you be happy to know that they get there in time to help load you on the ambulance, confident and proud that they meticulously obeyed all the traffic laws?