1991 Toyota Corolla damages caused by low oil

I had my oil changed a few days ago. The mechanic did not replace the oil cap. Last night the car starting making clanking noises under the hood and there was some smoke from under the hood. A couple of minutes later the car died. A man stopped to help. The man said that perhaps the car had thrown a rod. I had a container with a little oil and put that in the car.I was able to restart the car and pull it into a nearby parking lot.

I just called the place that did the oil change. Their position seems to be (1) that if low oil caused the car to die, then the engine would have seized and I could not have restarted it, (2) that if low oil had caused the car to throw a rod, I could not have restarted it. Basically, that their failing to replace the oil cap could not and did not cause the problem.

Could the failure to replace the oil cap and the consequent low oil have caused the clanking, the smoke and the car to die? What else could have caused it?