That's right. It's true.
Social Security is basically a pension plan combined with old-age insurance. Each person contributes money while working and gets back money in retirement. The government just does the accounting. To balance the Social Security budget, we only have to decide if we want more insurance (higher payments, same benefits) or less insurance (same payments, lower benefits). That's a decision we should make on its own, based on how much risk we want to pool.
Medicare is guaranteed health insurance that you pay for in advance. Eliminating Medicare wouldn't suddenly free us from a burdensome tax: seniors would still want health insurance, and since Medicare is better at cost control than the private sector, they would have to pay more for it. The real question is how much insurance we want and whether we want a guarantee today that we will be insured in old age. The amount we should pay for that insurance has nothing to do with the rest of the government. Instead, it depends on how much we would have to pay for health insurance otherwise--a lot and growing each year.
With both programs, there's no magical budget constraint that limits how much Social Security or how much Medicare we can have. We can have a generous program funded by high contributions or a meager program funded by low contributions or no program at all.
The crucial thing is that with Social Security and Medicare, we're not just hoping the government does something useful with our tax money. We are pooling our money to share specific risks across a large population, and that money comes right back out as pensions and health care payments. The size of these programs should depend on how much risk we want to pool, and nothing else.
Given that most Americans don't save enough for retirement and most working Americans with health insurance will lose it when they retire, I think most people will want more insurance, not less. We shouldn't be forced into less insurance by the delusion that government does one thing and has one size, let alone that it has to be smaller. Extending Medicare to all Americans would eliminate the plight of the under insured and uninsured, and it would be good for the economy.