At one time that was true and it is still the W. Brian Arthur's hot spot hypothesis of path dependency but hot spots always burn out and while sources of income Urban areas are also poverty sinks.
I'm not so sure. It's sometimes kinda intimidating how much the wealth is becoming concentrated into the cities, it seems to be getting to the point where city centers almost crowd out the non-wealthy and become inaccessible to anyone without a high skilled career or just lots of money.
Cities usually aren't "more" impoverished than the countryside, it's just that it's much more concentrated and as such more noticeable (there are exceptions of course, Aka, Flint MI). Most of the poorest areas of the country are quite rural and nowhere near big cities, like Appalachia or northern Maine.
