I looked up health care cost of the Duggars, and there was some confusion regarding Jim Bob's Health Care provider and whether, as a former elected official from Arkansas, his family's health care was paid by the Arkansas tax payers. However, it seems like he pays for their insurance, except for Josie who ended up on Medicaid due to being premature and in serious health risk. That is unlike that other "famous" family, the Bates. With the Bates, the Patriarch claimed that his family has no health insurance and they go to the ER for all their medical needs. Apparently, the medical costs are written off, so who gets to pay for those procedures?
I'm not usually one who will be quick to criticize people who find cracks in the system and take advantage of them due to a number of reasons, but I don't think it's quite accurate to say that the Duggars or families like them are totally self-sufficient and haven't benefitted from the system at a cost to taxpayers (local or national). At least the kids will pay into social security (assuming that they have jobs where their salary incurs a payroll tax).