The parent described the "top 10%" (chosen arbitrarily, I'm sure), and the only stats I could find described quintiles.
7.5% of the bottom 20% make it to the top 20%. In a perfectly fair and equitable society, you'd expect it to be 20%. I wouldn't call this "quite rare," though I would call this uncommon.
But what percentage of the bottom 10% do you think make it to the top 10%? It's probably even fewer.
And to go step further: I'm not convinced the "top 10%" actually has everything they need to become a billionaire. Zuckerberg's parents were both doctors, Bill Gate's dad co-founded a successful law firm, Musk's parents owned an emerald mine in South Africa. These folks almost certainly grew up in the top 5% of household income.
If you need to grow up as a child in a top 5% household to "have everything you need" to start a wildly successful company, what percentage of the bottom 5% make it to the top 5%?
I'll bet you it's indeed "quite rare."