It depends entirely who was at fault. If the bicyclist was at fault then the ambulance shouldn’t pay (which was one of the options I listed for why the ambulance’s insurance might not be paying), but if the ambulance was at fault then their insurance must pay. The article doesn’t state who was at fault from the police reports, so maybe fault was not determined there.

According to police reports, the driver who struck Hoesch and a passenger in the ambulance estimated the ambulance was going between 2 mph and 10 mph when they heard a thump, stopped and saw Hoesch injured. Hoesch estimated to police that he was going 5 mph to 10 mph and said he didn’t think the ambulance was going to turn in front of him. His bicycle was crushed under the ambulance wheel.

I would assume that if both vehicles were going approximately the same speed at the time of the accident, no more than 10 mph, that’s probably the steady speed for the bike but the speed the ambulance slowed down to for the turn. That would imply that moments earlier the ambulance was going faster and had likely just passed the cyclist moments earlier. Perhaps the driver was oblivious to the cyclist as they focused on where they were about to turn. It could be the cyclist’s fault, that he had sped up to pass a slowing ambulance on the right, but it seems more likely to me that the ambulance had just passed or pulled even with the cyclist and made a turn without considering the cyclist’s path.