Here is the conclusion spoilered if you want a TLDR
So there we have it! Pretty strong evidence in favor of Theory 3: the burger doesn't rot because it's small size and relatively large surface area help it to lose moisture very fast. Without moisture, there's no mold or bacterial growth. Of course, that the meat is pretty much sterile to begin with due to the high cooking temperature helps things along as well. It's not really surprising. Humans have known about this phenomenon for thousands of years. After all, how do you think beef jerky is made?
Now don't get me wrong—I don't have a dog in this fight either way. I really couldn't care less whether or not the McDonald's burger rotted or didn't. I don't often eat their burgers, and will continue to not often eat their burgers. My problem is not with McDonald's. My problem is with bad science.
For all of you McDonald's haters out there: Don't worry. There are still plenty of reasons to dislike the company! But for now, I hope you'll have it my way and put aside your beef with their beef.