If he wasn't a fireman then he certainly had fire training - He is the one who takes the extinguisher off Purley, as Purley does not know how to activate it. He then approaches the fire and uses the extinguisher correctly, spraying it at ground level from side to side from the optimum distance to maximise the effect of the powder and working towards the cockpit area of teh car. Once Purley takes the extinguisher off him he maybe thought Purley would know how to use it correctly. I am not sure how you would expect him to get the extinguisher of Purley again. Purley was the only person there who was wearing flame-proof overalls and he would have been better trying to move the car whilst allowing the other guy to use the extinguisher.
IIRC continental circuits at that time used local firemen as fire marshals, and they tended to be very protective over who used the extinguishers - even threatening to go on strike if non-fireman picked up an extinguisher.
In my view the reality is that it was a petrol fire and there was simply not enough extinguishant in the fire extinguisher to put it out, so the most that could have been done with the extinguisher was to buy Williamson some time, but it took the fire truck so long to arrive that it was always going to be too late, If they had righted the car they could have pulled Williamson from the flames, but there was only one person at the scene wearing clothing that allowed him to get in a proper position to push the car over onto its wheels (Purley), and he couldn't do it alone. If other drivers had stopped, it might have been different.
There is an interview with Williamson filmed on the day after the race where he says that although he had been angry about it the previous evening, he could now see why the other drivers didn't stop. If you think about it, each driver had a spli-second decision to make when they passed the crash site for the first time - stop or continue. They had to slow for the yellow flags but be mindful of not slowing too much in case the car behind should ram them, By the time the drivers passed the accident for the second time, it would have been too late anyway. Purley did say he thought the time taken for the fire truck to arrive needed to be looked into, and if I recall rightly he pointed out that the marshalls at the scene would have set fire to their clothes and ended up dead if they had got any closer than they did to the burning car.
For me, it's not worth criticising anybody who was there as they were working with totally inadequate equipment and safety procedures. It's easy to sit in front of a computer and say a man dressed in cotton and nylon clothing should have turned a burning car onto its wheels and pulled a man from the flames, but that might just as easily have made the consequences of the accident even worse. What still strikes me about the incident, though, is the sheer brutality of the fact that the race went on - the fire trucks arrived, they put the flames out, they tipped the car onto its wheels, put a blanket over the corpse and the race went on. It's like it wasn't even a big deal. I think the fact that those events were broadcast live in the Netherlands was something of a wake-up call to F1 that this something had to be done about this sort of thing, because those sort of pictures are the kind of thing that puts broadcasters, particularly state broadcasters, off motorsport altogether,