There's a lot of truth in this. It's easier for a middle-class person to be frugal and "stay ahead" of the game: Because I have a car, I can drive to the salvage store and buy food very cheaply. Because I have a freezer, I can stock up on bargain-priced chicken. Because I have good credit, I can buy a car for the lowest possible price. Because I can afford preventative medical care, I am less likely to end up in the emergency room for a minor problem like strep throat. The list could go on.
A person who's born into poverty CAN fight his way up out of a bad situation, but it's going to take more effort for him to become middle class than it'll take for his born-middle-class cohorts to stay at that level.
I think the biggest problem, however, isn't the increased cost of many of these individual things; it's the lack of awareness among the poor that it's both their choices and their circumstances that are keeping them in a bad situation. I don't think the situation is so bad that it's impossible to escape it.