It's deeper than that. Being poor often means you can't buy in quantity, and most things are cheaper in bulk. If you have to buy one can of soda for example, you're looking at $0.75 USD. If you can afford a little more, you can buy a 12-pack for $3.99 USD.
Or look at buying a home. In Utah the mortgage on a house is typically much lower than the corresponding rent would be, plus you build equity. However if you don't have the down payment or the credit to buy, then you have to rent. Your rent will be say $1,500/mo where as the corresponding mortgage would have been $1,100. It actually costs more for your housing because you are poor.
Whenever I say it's expensive to be poor, that's the kind of stuff I mean. Your options are just far more limited, in a way that makes it difficult to get a good deal.