... dude works for 20 years at minimum wage, and then when he gets sick with a non-acute ailment expects everyone to drop their shit and make his life better as a free ride -- and that's an example of "good planning done in by external forces"?

That summary is incorrect. He worked for 20 years at his chosen profession, lost his job, then found work at minimum wage instead of no work at all, then got sick.

Could he have saved more during those 20 years, and therefore done better? Undoubtedly. What size should an emergency fund be? Let's ask Google:

Though personal finance experts agree emergency funds are necessary, there’s no consensus on how much is enough. Some say you need save a year’s salary. Others believe $1000 is sufficient. Most advice tends to fall someplace in the middle.

says GetRichSlowly

Bankrate recommends creating a special account that you don't touch, except to pad it with 3-6 months' worth of expenses.

says LifeHacker

Most experts agree that you should keep between three and six months worth of your living expenses set aside in your emergency fund.

says About.com Financial Planning

Financial experts recommend that people maintain a cash reserve large enough to cover three to six months' worth of household expenses.

says Investopedia

Enough money to deal with major medical expenses following a prolonged period of un- and underemployment.

says... um... nowhere, as far as I can tell.