I acknowledge that there is plenty of really cheap junk "food" out there, there is also plenty of healthful food out there that is cheaper than common low-quality foods. Even soda pop is more expensive than water (fill a bottle from your tap).

To continue with that theme, any prepared food is relatively expensive, and relatively unhealthy. If you want a high fiber, high protein, low-fat, low-sugar meal...then cook some rice and beans. Stick some spices in there, and maybe some cheese. It ain't that bad. Fresh produce is rather expensive, but you can get good deals on frozen/canned vegetables. 

 I don't think that the problem is that good food is expensive...it's that bad food is accessible and so tasty.

Multiple studies have shown that if you're eating on the cheap, your diet is going to suck. The price of fruit and vegetables has gone up signficantly over the last few decades, while the price of candy and soda continues to fall.

There are two issues here, and to make sure we aren't talking past each other, I want to be explicity about them:

1. Bias in food choice: I agree that cheaper junk food will result in greater consumption of junk food. This applies to anyone who is at all price sensitive, and probably applies more to the poor than to the middle class.
2. Necessary constraint on food choice: I disagree that our food markets are structured such that a person has to rely on "junk food" to get by. I agree that fresh produce is inaccessible to the poor, but that does not leave them to only eat sugary and fatty foods. In my market, complex carbs and lean (vegetable) proteins are no more expensive that simple carbs and fatty proteins. I don't think that poverty would force a person to eat junk food just based on the prices of the commodities. If poverty is going to necessarily disrupt a person's nutrition, it will be through lack of access to:
1. fresh produce (as stated before)
2. a kitchen
3. a grocery store
4. nutritional knowledge
5. time to prepare food

Focusing on your second point.

We agree on the limitations on fresh produce, kitchens, grocery stores, nutritional knowledge, and time to prepare food. All of which will cause problems for the diet of those in poverty.

I would argue that the net effect of all this is to make junk foods cheaper than healthy foods. I'd also add food insecurity, which will impact metabolism.

But when you subsidize corn to the point that HFC syrup based soda is cheaper than water, or your cheapest meal is a McDonald's burger, there's going to have an impact.

...just that being poor doesn't mandate that a person eat junk food (as was implied by the comment that junk food is cheaper than non-junk food).

If poverty is going to constrain a person's access to food, it will be due to lack of:

1. Fresh produce
2. A functioning kitchen
3. A local grocery store

 Based on the prices in my local grocery store, fats and simple sugars are not a less expensive source of calories than complex carbohydrates. Likewise, fatty protein is not less expensive than lean (vegetable) protein.

I shop at either Harris Teeter or Whole Foods, which caters more to my preference for healthy foods, but is much more expensive than the likes of, say, Food Lion, which offers cheaper prices but doesn't even come close to offering the healthy food alternatives that I expect as a shopper. Your making the point that the dedicated but poorer shooper can find what he needs at the likes of, say, a Food Lion, and I don't dispute that, but good luck in any Food Lion shopper maintaining such dedication to a healthy lifestyle by shopping at Food Lion. It just isn't happening...