It's not really "their choice." Try eating well when you live 2km away from a grocery store, work 2 jobs and have to consider a bus ticket's impact on your budget. Unless you're very determined, you're going to have fast food.
First off, buying groceries and cooking is a huge money saver - if you're worried about the cost of public transport, the savings you get from cooking are also on your mind - you can easily eat healthy meals with plenty of meat and vegetables and still come out x3 cheaper than fast food here(never mind having to eat out - you're looking at x5-x10!)
It doesn't take a lot of effort to cook, once you get over the mental hurdle. Most of the meals I know how to make are a variation of "put stuff in container, apply heat", all taking 10-15 minutes to prepare. Another 10 minutes of chopping up a variety of vegetables for a salad and you have meals for several days straight, if you're living alone.
Speaking of living alone, that's just not my experience. My family grew up poor, and lots of my friends lived on shoestring budgets. Everyone lived with their parents, their roommates, their new family. They shared stuff and helped each other out. The parents around the block I grew up at saved a lot of time by taking turns to invite all the neighbourhood kids for a dinner at a single place. My roommates would take turns cooking, and we'd all go on a single shopping trip during the weekend, everyone carrying bags home because taking the bus was a luxury.
I'm not saying that given a set of circumstances, there aren't people who are capable to pay for fast food, and forced into doing so. What I am saying is that these circumstances arise over a lifetime of choices(not necessarily just theirs), and at some point you have to throw up your hands and say "well, stop doing that".
Every time I've visited Europe, I've been able to find a Monoprice (or a Carrefour, etc.) within walking distance of my hotel. They all had fresh meats and vegetables at reasonable prices. Nothing similar exists in most U.S. cities.
I have lived in poor rural America. Here is some information for you that might help: There are no forms of public transportation. You are required to own your own car or have someone drive you. Work is usually 1 hour or more away. The grocery store is usually 30 minutes to 1 hour away. There are usually fast food restaurants within a few miles. Don't forget that America is gigantic in area and very spread out in the rural areas. However after telling you this, when I was a child we did go grocery shopping and ate things like crock pot roast beef and hamburger helper.
A lot of people have inconsistent access to both of these. They may not have a fridge at all; they may only have a microwave. Or they may have a fridge and a cooker, but not have the money to pay for electricity to run them.
Most poor people would benefit not from fridges, but from freezers. These allow you to buy frozen veg and keep it for a few months, and they allow you to batch cook and freeze.
> beans and rice are cheap as hell and nutritionally complete,
Absolutely not nutritionally complete - you're missing vitamins A & D and some minerals (eg, calcium).