Auric, you can argue that the traffic laws serve the side-street traffic in this case: by keeping people from running the red light in their direction and causing an accident. You don't have any idea how serious the situation is back in the ambulance, so you don't have any a priori basis for endangering the cross traffic. Just playing devil's advocate
I have run red lights in the past to get out of the way of an ambulance. Usually if traffic is snarled enough for an ambulance to get behind traffic, the cross-traffic in the street also stops when they see the emergency vehicle, so there's minimal danger involved with running the stop sign.
99% positive that you'd be liable for an accident if there were one, though...