Having lived in a few other countries with less industrialized distribution networks, no, this claim is dramatically incorrect. Fruits, vegetables, staples like rice, and basic forms of protein (fish, insects and sea critters, some chicken) are much, much cheaper relative to processed foods. Larger protein sources like beef, pork, or bushmeat is relatively more expensive, however, unless you opt for poor quality processing like cheap "corned beef" made from offal.
As an economist, I appreciate the difficulty of making apples-to-apples comparisons across countries for things like food prices, as even the acclaimed "Big Mac Index" assumes that a Big Mac has a similar relative status across countries (though the oft-misunderstood intent of the Big Mac Index is to more to compare consistent production costs). In some places a Big Mac is fancy, in the US it is considered fairly garbage but consistent.
For example, in a market in the Philippines, you have mostly cash transactions and informal capture for what the majority of people purchase. The purchasing is done more in these almost farmers-market style transfer versus grocery stores in the US. They _do_ have grocery stories, but almost uniformly for processed food distribution versus fresh food in the markets. It's much cheaper to eat healthier from the markets and through the informal distribution network of sari-sari stores versus equivalent nutrition from processed food from the grocery stores.
Also, consider the results of this recent study: https://arstechnica.com/health/2025/08/in-trial-people-lost-...