You are correct, and not only that but the free flow of poor people is limited by regulations that prevent low cost bus and taxi services from entering the market. There is no reason that poor people with jobs in suburbia couldn't ride in a van owned by another person looking to earn some money. In fact it could be a pretty good business. If you watch carefully in certain areas you will notice, for example, vans carrying Asian workers from the city to the Asian restaurants in the suburbs.
Forty years ago in Philadelphia old re-purposed school buses came to pick up inner city residents who wanted to work on the farms in New Jersey. I'll bet regulations today would make that kind of transport impractical or even illegal.
Krugman and his liberal allies do everything they can to stomp out businesses like that which actually help low income people improve their circumstances. And then they complain about the results of their efforts.
Around here, there are vans that pick people up in the evening to take them worm-picking at the farms to the north, then return them to the city in the morning.