"It's why athletes who take rest periods or have injuries are able to come back just as strong in only a few weeks."
It's more complicated than that. Actual muscle mass has less to do with being strong than leverage and nervous system development.
Leverage is genetic and there's not much you can do about having long arms.
What you call "muscle memory" is the strength and frequency of nervous system signaling - most strength gains come from changes in the nervous system.
That's why there's tons of drug-free power and weightlifters who don't have a ton of muscles but are extremely strong. Conversely, there's tons of bodybuilders using steroids who can't actually lift all that much. This is because muscle mass is mostly dependent on hormones.
You don't gain muscle by lifting weights so much as you raise your testosterone level by lifting weights, which promotes muscle growth.
So athletes can come back quickly in terms of strength, but not so much size.
From what I read about Tim's "muscle gain" advice (he posted the story on his blog) it was mostly just water and fat. I bet he started out by dehydrating before the experiment, too. Assuming you start out slim it's very easy to gain 34 pounds in a month by drinking water, eating a ton of high-carb foods and taking creatine (I've done ~20 pounds in two weeks this way to go up a weight class). The only way you're going to gain any muscle that way is with weightlifting (a lot more than 4 hours) or steroids, and preferably both.