Our OP fell off as a result of his own failure to leave a suitable clearance between himself and the vehicle he was following. That vehicle is entitled to be able to brake for any purpose with the reasonable expectation that a vehicle following won't plough into him or otherwise come a cropper as a result of trying to avoid them. Therefore, I would suggest this is a result of the riders own poor judgement or inattention, and not the result of the presence of a motor vehicle on a road or other public place.
Just because a motor vehicle was present and on or highway or other public place does not automatically make that vehicle at fault for other incidents in the immediate vicinity. It's neither car 1s or car 2s problem if vehicle 3 does not leave a gap in which they can safely stop if required to do so. Car 2 was traveling at a speed and distance that allowed him to stop in the distance he could see to be clear - vehicle 3, for reasons not known, failed to observe this oft repeated, and frankly quite sensible, mantra.
Car 1 pulled out, a manoeuvre that may have been Ill advised, dangerous, or even unlawful.
Car 2 spots this, safely stops.
That incident then ended at this point.
A further incident occurs when vehicle 3 loses control as a result of trying to avoid car 2. Car 2 is commuting no offence and doing nothing untoward. There is now no connection with Car 1.
Go have a cup of tea, lick your wounds, and learn to leave a safe gap to avoid future face planting.