I think maybe he's saying that sometimes, one person can slip through if the appropriate conditions are met. Your implication is correct as well. He offers only an anecdote to back up the claim, but no data. Even assuming the anecdote to be true, and s/he has multiple childhood acquaintances from poverty who each now have a 5.8 million dollar or higher net worth [1], it would have little effect at the mean of the population.
Personally, I think the explanation is structural, or if you prefer, just math. Just statistical distribution will assure that if you're poor, 99 percent of you won't get into the 1%. You'll never amass the required 5.8 million dollar net worth.
In fact, I almost hate to say this, but it should be implied, whether you are poor or middle class, 90% of you will never even get into the 10%.
I'm not sure that it's a psychological state of mind, or even a statement on the innate abilities of poor or middle class people? I'm more confident that it's a simple structural barrier. There is not room in the 10% for every law abiding, intelligent, ambitious, hard working individual. Which means many law abiding, intelligent, ambitious, hard working individuals who are poor or middle class, will need to aim lower to increase their chances of success. It sucks, but just in my opinion, that's how things are, I'm not sure there's a way around it?
So I think what's happening is more along the lines of people, perhaps even unconsciously, realizing the structural reality, and adjusting their strategies accordingly. That poor or middle class kid says:
"You know it's a lot safer if I just become a nurse, teacher, or regular software engineer instead of trying to swing for the fences on a startup since I have no safety net to work with."
In fact, in a societal moral hazard kind of way, the more intelligent and rational that poor or middle class kid is, the more likely s/he is to say that. (Or maybe it isn't a societal moral hazard? Since we do need nurses, teachers, fire fighters, and so on. I don't know?)
[1] Net Worth of 1%-er: https://money.com/richest-1-percent-america-other-countries/