The comments by Martin Shkreli I was referring to are actually in the video that you linked. The subtlety in Shkreli's comment is that he was referring to amassing "fortunes". That is where he states that amassing fortunes most likely requires using "other people's money". Which makes sense.
He cites Joe Lewis as an example of a solo investor going from "zero to hero", but I would not say he was strictly an "investor" as he was a currency trader. Also, he had initial wealth from a luxury goods business.
Just for curiosities sake, do you know of any examples of retail investors amassing sizable amount of money starting from very little?