That depends on how you define 'wealthy.' There is a vast gulf between the kind of money people of sound mind and body can get through hard work and the degree of wealth the truly rich actually own.
The guy who grew up in a ghetto but is now making a six figure income (anywhere but San Francisco) did it mostly though his own hard work. I would not, however, call that guy wealthy when compared to the truly rich.
The 40 people who own more wealth than the bottom 50% of the US population own it by virtue of being born to the right parents. There is no degree of hard work that will make someone a billionaire. Those people got that far by being born into a family that could give them seed capital and access to elite education that enmeshes them into the right social networks.
When people talk about income inequality, they're not talking about people earning $500,000 in wage income by working 80 hour weeks. Instead, they're talking about people who are extracting a tens of millions of dollars in economic rents (as largely untaxed capital gains) without needing to do any work for it.