In low cost of labor countries, I've seen the exact opposite. It's probably not very profitable in the US to setup a vegetable stand for 12 hours a day along a highway for $10/hr of sales. In many countries it is - you have a market garden and put one of the grandparents/children/cousins/etc. manning the retail operation. A single western tourist can make your entire day profitable (including opportunity costs) assuming no other sales.
In my experience you pay a huge premium in the US for locally grown (e.g. weekend farmers markets) - but in other countries it's the opposite - supermarkets are pretty expensive, and the "local farmer" markets are a quarter of the price.
Large supermarkets, etc, can get access to these ridiculous prices and so it can cause prices to stay fairly low. However, it is not really healthy for the farmers. If you live in a really rural area that doesn't have access to a large world-wide market, the local food will be a lot cheaper because the only outside food you have access to is super expensive.
For me, buying local is about agricultural sustainability. It's about making sure that my neighbours can grow food, sell it and live comfortably. I'd also rather have many small farmers producing the best quality produce they can, than 1 super farmer that is trying to produce the cheapest produce they can. This all adds up to higher prices, of course.
I often feel that we should have "fair trade" in food everywhere. I can buy a pound of raisons from California for less than $2. The same grapes would be 4 pounds. $2000 of raisons at a retail price is 4000 pounds of grapes... And you think for those tonnes of grapes... how much is the farmer getting? It gets a bit crazy.
Is this true? In my experience the cheapest food is rarely almost never locally produced. It may be marketing and the demand for local food is higher.
Long supply chains have a lot of value add. Sure there is cost to transporting and storing the food, but the process has other efficiencies that more than make up for the cost. I've even read stories about Central American countries exporting their produce only to reimport it back for the locals to conusme.