No chance. If he sped up, it was to try and avoid the collision. There's no way he could see a car running the light. If cars could see that, they'd stop before the got in an accident.
Also, as to the peds crossing with a green turn arrow: I don't get this, but I see this in PA all the time. Cars get a green arrow to turn left and at the same time, the peds get a white walk sign. So the car pulls forward into the intersection, but has to stop because the peds have the right of way. By the time they all cross, the light has turned red and only one car gets through the light. So stupid.