Independently dependent?

in-de-pend-ent: (adjective) not relying on another or others for aid or support; sufficient to support a person without his having to work.

The concept of being "independently wealthy" fascinates me. The whole thing just seems a little oxymoronic. I get the idea of a person having enough money in the bank to not have to work full time, or need a full time income for support, but chances are that money was made not by the independently wealthy person, but by the parents. So doesn't that make the "independent" person dependently wealthy? Unless maybe you hit it big in the dot-com era and socked oodles of money away, I really don't know anyone in my generation who could be independently wealthy on their own wealth. So what happens if daddy pulls the plug?

In all fairness, I only know one person who is independently wealthy and I don't even really know her that well. She does work, but not in the 9-to-5 grind as most of us do to support ourselves. But she's got enough to live quite well. And it came from her parents.

So is "independently wealthy" just the grown-up term for "born with a silver spoon in the mouth"?