Doesn't your observation that most successful autodidacts come from financially stable backgrounds SUPPORT the hypothesis that intelligent individuals from low-income backgrounds are prevented from becoming successful?
With the facts you've highlighted, two conclusions may be drawn: either most poor people are stupid, or the aforementioned "starving farmers" don't have the time or the resources to educate themselves or "[bang] out some impressive proofs," on account of the whole "I'm starving and need to grow some food" thing. I don't see how such people would be able to afford books to learn from or time to spend reading them.
Thank you very much for this. Until you put it this way, I could not grasp the Monty Hall problem; I persisted in believing that there would be a 50/50 chance once the door was opened. Thank you for changing my mind.
I'd say it's highlighting the human fallacy to try to ignore and escape from bad news. Instead of facing this prophecy, they just destroyed the ship that delivered it to them and told themselves they were safe.