[probably_wrong]

I recognize I'm completely ignorant about this topic so I have to ask: how does the theory fit within the story in the post?

If I understand you correctly, mutual aid theory explains the author buying cheap forks just to do something good. At the same time, in the absence of penalties people will steal forks until barely any remains. So why should one believe that the balance will favor the fork buyers more than the fork stealers?

[yareal]

The basic theory is that when something is abundant and everyone has what they need, the incentive for theft doesn't really exist. If you set out a barrel of forks and say, "take what you need" then at some point everyone has taken as many forks as they need. If we assume this is also happening for other bulk items, and everyone can just have as much as they need, there's nothing to trade those forks for, so taking a bunch doesn't benefit you at all.

Ask yourself, why would you take more than you need? Not some hypothetical other person, but you, personally. Do you think other people are in general likely to behave like you? (Put another way, do you think you are fairly typical when presented with a "take what's fair" scenario?)

It's like the candy bowl at an office or someone's house, or the "take a penny" cup at a store. I'm sure occasionally someone takes everything from it, but by and large people take what they'll personally use.