I think this is only true if you adopt a very narrow definition of "successful entrepreneur".
If you're looking at non-US, or non-technology entrepreneurs, I think you'll find that this conception of an entrepreneur doesn't fit. (E.g., see this article on global entrepreneurial activity https://grasshopper.com/blog/where-do-most-entrepreneurs-com...).
Even if you're talking about non-US, tech entrepreneurs, I also think this definition falls apart. The many, many new super-wealthy tech entrepreneurs coming out of China and India grew up in a time when neither country was particularly rich.
People engage in entrepreneurship for numerous reasons, but I think it's foolish to discount the sheer number of people who do so out of financial necessity, i.e. the need to earn enough money to put food on the table and support your family.