Here's my understanding of what happened - they were going down Calhoun st to an unconscious, took the opposite lane to get through the intersection, and then railed the victim's car, which was in the turning lane, as she turned left. At that time of day there's a decent amount of traffic, and I would never be comfortable travelling that speed for any reason whatsoever.
So, the victim was turning left at the intersection, which was green at the time, from what I've been told. Now, if the ambulance was following the SOP regarding speed, they would have had enough time to slow down significantly (from 35 mph, not 51.6), greatly lessening the impact, if not avoiding an accident altogether. It's entirely possible that the victim never saw the bus, as they may have swung out from their lane across the double yellow, while the driver was checking the intersection for other cars, not an out of control emergency vehicle coming out of nowhere.
Really, how many of us in our POV's are checking the rearview mirror when executing a left turn in an intersection? We're checking the light, pedestrians, and oncoming cars coming the opposite direction (in front of you, not behind you going the wrong way. Next time you drive, make note of where you instinctively look.
My dept SOP's allow us to exceed the speed limit by 15 mph on the road or highway. We must slow to the posted speed limit at a minimum when going through intersections with a green light. Highway on ramps are whatever the posted speed limit is. Stop signs and red lights require a complete stop. All of this is with the caveat of "due regard". Besides speeding, this EMT didn't exercise due regard. He was driving so fast (down a busy street) that he pushed the victim's car through the intersection, pinning it to a parked car on the other side of the intersection! A long cut job ensued.
When driving, one should never make a move that they can't get out of, should other drivers do something unpredictable. Simple as that.