In a city where everybody makes a lot of money, prices rise so high that the moderately rich live like middle-class people. Just because the United States has a dozen of these communities doesn't mean that $200k is middle class.
Also, if you make enough money that the interest/capital gains on your money is enough for you to live on, you're rich. Never in the history of the world have people made enough money that they could stop working (without government help, anyway) and not been called "rich." Just because you're bad with your money and blow it all trying to have the most expensive stuff doesn't make you middle class.
Put another way, it's stupid to define rich as "having more money than you could possibly spend." As we've seen with powerball winners, people can spend a shitload of cash if they're undisciplined with their finances.
Obviously, it's extremely difficult to develop objective criteria for the boundaries marking off middle class (or, perhaps, the middle classes) from rich and poor. Poor is obvious: if there is a legitimate concern that you may not be able to afford food until the next paycheck, you are poor. Rich is somewhat more difficult, mainly because it's somewhat of a taboo in this country to admit that you're rich, but there's one solid criterion: if work has never been a necessity for you, you're rich.
The problem with our discourse hinges mainly on the fact that there is a group of people who do work or have worked but should by most standards be considered rich. Because of said taboos, however, we allow them to call themselves "upper middle class" (and even "middle class" in some cases) and they skew perceptions of economic class because they don't really belong in the same group with everybody else.
The median household income in this country is $48,201. If your household brings in $60k, you're in the 60th percentile of income earners (as in, 59% of the country makes less than you). If you would consider a 60k/year home to be "poor," you're probably rich. Yes, even if you live in New York, and even if you still have to work, and even if you're living paycheck to paycheck because you're still paying off the million dollar house and the Land Rover and your kid's private school and the credit cards.