While I won't argue that fast-food diets are healthy, what this shows us is that McDonald's food acts like any other food when it is cooked in a way that drives water out and kept in a dry, airy environment: it dries up and stales, instead of rotting.
Notice that the burger, fries, and chicken above are relatively thin, with a great amount of their surface exposed to air. Note also that they're fried with high heat, which is a cooking process that removes a lot of moisture from the food, and that they're high in fat, which also means less moisture in the food. Third, note that they're kept in the open air wrapped in paper and not in a plastic bag or other airless environment.
Rot and molds need moisture to work. Give them a thicker burger, chunky fries, and a whole grilled chicken breast and they'll go to town on it. Give them a dried-out piece of meat, skinny fries, and small deep-fried chunks of chicken and they will have little action, if any (although storing them in a Ziplock bag with no air circulation will let them work).
Short version: it's not processing or artifical preservatives keeping these foods from rotting, they're just drying out due to lack of moisture. Avoid these foods because of the high fat and salt content, not because of misleading shock tactics resulting from a misunderstanding of natural processes.
Scientists explaining the results: http://www.salon.com/2010/09/01/burger_that_wont_rot/
Someone replicating the experiment, controlling for various variables, and comparing to home-cooked burgers: http://aht.seriouseats.com/archives/2010/11/the-burger-lab-revisiting-the-myth-of-the-12-year-old-burger-testing-results.html
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