Then I know a lot of people with >$30 million who are not rich, and I know a few with <$1 million who are rich.
That doesn't make your definition wrong, but it does point out that being rich is a matter of personal choices on expenses just as much as income/gross worth.
If you go to West Chester county NY you'll find hundreds of ex-Wall Street guys with foreclosures on their 5 million dollar houses and annual salaries >400k and little to show for it after the crash.
Not having to worry about money, and working by choice rather than out of necessity.