You're misinformed. Cheap healthy options are readily available at the grocery store. If you don't want to spend time on food preparation you can substitute canned vegetables for fresh which is slightly less cheap but still cheap.

In the extreme case you don't even need a proper kitchen - a microwave, a rice cooker, and some large bowls will suffice. You can reliably find all of those things at thrift stores in the US. You also have the option to purchase dry staples in bulk (rice, oatmeal, pasta, etc) in 10, 25, or even 50 lb sacks if you can find a local place that stocks them (costco for example).