Emergency responder (fire/paramedic) here. EVIP (Emergency Vehicle Incident Prevention) is a course that in most states, responders are required to take to operate a vehicle in "emergency mode" (i.e. lights, sirens, both). In some states it also serves as a replacement/alternate for requiring a CDL for larger vehicles.
In "emergency mode", the vehicle, based on most state's laws or administrative codes, "may ignore any and all rules of the road, including but not limited to, speed limits, traffic control signals, designated lane markings, one way directionality". Quite simply, on the road, in emergency mode there is no "obeying traffic laws"...
BUT...
What the words give you, the fine print often takes away. While in emergency mode, the driver of the emergency vehicle is -presumptively liable- for ANY incident that occurs, unless it can be demonstrated otherwise (and even then there is still likely to be contributory liability). This liability is personal and organizational (i.e. I can be personally sued if I hit someone in my ambulance, even going code 3).
To mitigate this, in additional to the department/organization's own insurance coverage (often self-insured by the appropriate government entity) will draw up their own department policy that applies intermediate limits (i.e. while the admin code may allow me to drive at any speed I like, our department policy says I may exceed the speed limit by no more than X mph, and X is reduced by 5 for every complicating factor, like night, or weather). The department will then take a separate insurance policy that says as long as I am within department policy rules, they will cover any personal liability that may occur.