Not 100% true.
Right now, I'm on a limited income. I have less than $2000 a month to live on because I have cancer and can't work full time. I am paying medical bills. I still manage to buy mostly organic by budgeting carefully - eating mostly vegetables, rice, beans, etc. I do have a pastured egg every day. How do I do it? I don't buy processed food, I don't go out to eat, I don't buy alcohol or Starbucks, I don't have any streaming services or cable, etc. I cut everything to the bone so I can buy myself healthy food.
I grew up in New York City. My parents were working class. Mom always made us healthy meals. How? She cooked everything from scratch. Clipped coupons. Bought veggies from the Indian grocery store.
Most cities have ethnic markets and you can use public transport to get to them. When I was in grad school and broke, I went to the Chinese market in Denver. It was located in a poor neighborhood but was a great place to get affordable produce, herbs, fresh seafood... most of it is not organic but if you guy whole foods adn cook meals from scratch and stick to mostly veggies, beans, and rice - you can eat healthy. I did this in grad school, and I budgeted carefully so at least I could buy organic eggs, milk, and yogurt.
If someone is on welfare and is paying $200 for sneakers... well, their priorities are different than mine. I had a friend who was in grad school and spent money buying video games and ate crap. Another person I knew complained they couldn't afford health insurance but they always bought booze and cigarettes. Which is fine. Everyone has to make the choices that work for them. No judgement from me.