Every jurisdiction I have ever heard of (in the United States, at least) allows emergency vehicles to disregard traffic rules when they can do so safely. This is why you will often see that speeding police/fire/EMS vehicles with lights and sirens activated will still slow down for intersections, and then speed off once they have safely cleared the intersection.
The officer in this case was probably permitted to drive as fast as they were driving, and to drive through a red light, however they had a superseding duty to operate their vehicle safely. It doesn’t matter what kind of an emergency they’re responding to, that doesn’t give them the right to cause harm along the way. If the officer could not know with reasonable certainty that they would not collide with another vehicle (or pedestrian) when going through that intersection, then they shouldn’t have proceeded through the intersection at that speed.
Similarly, police officers are permitted to carry their guns under circumstances where most people would not be allowed to carry a gun. However, if they accidentally shoot an innocent bystander, they are still liable for that shooting. They can’t go waving their gun around just because they’re allowed to have/use guns under specific circumstances. Sounds like an extreme example, but cars can be just as deadly as guns.