Formaldehyde
Both Fair And Balanced
The ambulance's lights were on (patient inside).
The only time an ambulance should be running emergency is when either responding to a call where a life is in jeopardy, or when transporting a patient to the hospital under the same conditions. I seriously doubt that heat exhaustion was sufficent reason for the latter.
The ambulance driver also would have likely not stopped, and the cops would have likely never caught him after responding to the emergency if that was the case. The emergency lights would have also likely still been in operation after he stopped. They were off in the video.
The dude following the ambulance would also not likely been able to keep up so he would not have been there to take the video. You also have likely heard him shouting "my mother is dying and you are trying to give the driver running emergency a ticket?!?" So no, I think he was running with his lights off when he got pulled, which also means the cops would have no way of knowing he was transporting someone to the hospital.
An ambulance is also not the easiest vehicle to drive. There is no rearview mirror so all you have to work with are your side mirrors. Unless the cops running emergency approached him from the front, it is quite possible that the driver didn't see them, especially if they were running without sirens which is quite typical if they want to maintain relative secrecy when they were approaching the scene.
It is also quite likely that the car in front of them that suddenly slowed did see the cops approaching, which would have exacerbated the situation even further. He may very well have had to make an avoiding maneuver because an ambulance is also not the easiest vehicle to stop on a dime. It takes a far longer distance to stop than a passenger car takes.
So bottom line as I see it: The cops should have backed off when they determined that the driver was busy transporting someone to the hospital. If they really wanted to harass him further, they should have followed him to the hospital and dealt with him afterwards. To try to arrest him under those circumstances is ludicrous, and it should result in at least one of them losing their jobs. Bad cops, no donuts.