I don't believe Elon had any more undue privilege than any other Stanford graduate. (Which is not none, but it means none of the emerald stuff matters.)
There's no need for any such influence anyway, getting rich from PayPal is already pure luck and you should be satisfied complaining about that!
What I am doing is falsifying your hypothesis. If being born to rich parents, having connections, and going to boarding schools is the sole reason people get rich, then we would expect that people with richer parents and more connections who went to better boarding schools than Elon Musk would be richer, and people who grew up in similar conditions to Elon Musk would be equally rich. This is not true.
No, I’m looking at two “lottery tickets” with the exact same numbers and asking why one of them one the jackpot and the other one didn’t. The only conclusion: it’s not a lottery and what you have picked out as the winning lottery numbers are not that.
> how does being the son of a guy who owned an emerald mine in South Africa explain him being richer
That's faulty, a posteriori reasoning.