I took it to mean that there were no insurance options outside of employment, which isn’t the case given 国民健康保険 exists. IIRC, a lot of people doing バイト and パート in addition to students and unemployed are on the same (or a dependent, which relies on their spouse/parent/etc.)

EDIT: Also, I think employers or a certain size (or maybe just 個人事業) don’t have to provide health insurance, but I’m not 100% on everything around that off-hand.