It comes down to your & Brian's definition of what "self-made" means.
I believe in the studies of millionaires, "self made" means they did not inherit their money, not that they didn't have some advantages that many others did not have.
Side note on luck (and not on the broader discussion).
I'm of the belief its not all/mostly random chance, you can influence how "lucky" you are. See below study & article on another study.
As Luck Would Have It - Scientific American
https://www.washingtonpost.com/welln...d-real-change/