It has nothing to do with legal organizations or capitalism, it's basic logic.
The basic logic is that if you don't eat, you will eventually starve to death. You might get by for a while on stored fat (savings), but eventually your body will begin to consume itself (debt) and eventually die (bankruptcy).
Sometimes there are other inputs, which aren't as "from nothing" such as car parts or oil. But skilled labor is still a necessary component, to turning those components into a working car that is more valuable than the parts or oil.
And sure, some of those "not from nothing" components are absolutely non-negotiable for survival, like people having to eat and be sheltered. But I think it's pretty clear that a skilled laborer like Henson is able to give more value from his labor than he consumes in food and board.
The corporate model you're shoving everything into assumes we have to put a dollar value on everything and that dollars in versus dollars out has to line up, but forcing a service-based charity into that model is an impediment to its effectiveness. The entire point is to give as much as you can, even if that means giving more than you take.
And that makes perfect sense, by itself, without having to represent it in a balance sheet. And the only way you can shoehorn it into a balance sheet is by ignoring the entire point.
For an organization to output something of value to people they will generally need something of value as input. Money is the best way to convince someone to give you that input. Money is burgers, beers, drugs, and gasoline. Something you can sell for money or barter is a close second. There are other ways to get that input, but ultimately you are relying on someone being convinced into doing something for less in return than what they put in: military draft, patriotic enlistment, prison labor, slavery, volunteering, donations, taxes, robbery, inflationary money printing, non-competes, anti union laws, a nationwide campaign to convert to communism, etc.