The Clinton campaign's assault on Bernie Sanders over health care got more intense on Tuesday.

This time it wasn't presidential candidate Hillary Clinton or one of her aides delivering the attack lines. It was her daughter, Chelsea, who argued that Sanders would dismantle Medicare and Medicaid -- and "strip millions and millions and millions of people of their health insurance."

Like so many statements the Clinton campaign has made about Sanders position on health care, Chelsea’s contained some true statements -- and some wildly misleading implications.

For the last few weeks, Clinton has been attacking Sanders over his longtime advocacy for single-payer health care. That's a system in which everybody, or almost everybody, gets insurance directly from a government-run program.

Countries like Taiwan, Sweden and Canada have single-payer. The U.S. has a version of it in Medicare, which serves the elderly and disabled. Many progressives have long dreamed of extending it to everybody else. Some even call it "Medicare for all."

During his Senate career, Sanders has repeatedly introduced single-payer legislation -- most recently in 2013, when he introduced the American Health Security Act. And while Sanders has also voted for less ambitious measures, including the Affordable Care Act, he has always envisioned those initiatives as incremental steps toward a single-payer system.

That has made him a hero to many liberal voters. It has also drawn the wrath of the Clinton campaign, which has attacked the scheme in two separate ways -- each making a factual claims and then leaving out critical context.

Because a single-payer plan would require the government to raise literally trillions of dollars in revenue, Clinton has assailed Sanders for calling for a massive tax hike. That's true. What Clinton never mentions is that those taxes would displace existing private insurance premiums.

And because Sanders' version of single-payer envisions separate state programs, Clinton and her allies have suggested that hostile state officials could thwart his plan. That's also true. But what Clinton never adds is that Sanders' scheme would also impose regulations, limiting state leeway over who to insure and what kind of coverage to supply.

During a campaign appearance in New Hampshire on Tuesday, Chelsea offered a version of these arguments -- but went a little further.

"Sen. Sanders wants to dismantle Obamacare, dismantle the [Children's Health Insurance Program], dismantle Medicare, and dismantle private insurance," she said, according to an account from NBC News. "I worry if we give Republicans Democratic permission to do that, we'll go back to an era -- before we had the Affordable Care Act -- that would strip millions and millions and millions of people off their health insurance."

It's true that, under a scheme like the one Sanders envisions, most people would lose the insurance they have today. But that's because everybody would have the new government-provided insurance instead. And while the transition from the old system to a new one would be far more complicated than single-payer advocates like to acknowledge, the whole point of a single-payer plan is to make sure that coverage is simpler, more comprehensive and more reliable than it is today.

If anything, a single-payer plan like the one Sanders envisions would result in more coverage than current arrangements would allow. The Affordable Care Act has produced a historic reduction in the number of people without coverage, but something like 9 or 10 percent of Americans remain uninsured. One reason is that the system depends upon people signing up for insurance. The Sanders bill states quite explicitly that "every individual who is a resident of the United States is entitled" to insurance, and then requires the states to enroll people automatically.

Characteristically missing from Chelsea's comments was any recognition of these facts -- or acknowledgment that Sanders has a long record of arguing that people need more protection from medical bills, not less. Maybe the most generous interpretation of Chelsea's comments is that she was making a political argument: that, by calling for single-payer, Sanders undermines enthusiasm for the Affordable Care Act and makes it more vulnerable to repeal. But Sanders has been a loud, consistent critic of GOP efforts to wipe away the law. It's hard to see how that constitutes giving "permission" for repeal.

Clinton campaign spokesman Josh Schwerin stood by Chelsea's comments when contacted by The Huffington Post.

"It is risky to try to replace the Affordable Care Act, CHIP, Medicare, Medicaid and TRICARE with a new plan that counts on Republican governors who have already rejected Medicaid expansion to foot some of the cost of care," he said. "And it has the potential to cause disruption in health care for millions of Americans who just got covered."

Clinton of all people should be sensitive to misleading attacks on health care plans. As a chief architect of the universal coverage plan former President Bill Clinton proposed in 1993, she confronted all kinds of outlandish claims. Most famously, one conservative commentator claimed falsely that this health plan would force doctors to go to jail if they refused to accept the new, government-regulated insurance.

Health care was also a major issue in the 2008 Democratic primaries. At the time, Clinton supported an individual mandate, which requires that everybody get insurance or pay a fine, and then-Sen. Barack Obama did not. When Obama's campaign sent mailers to Ohio voters, warning them that Clinton would force every single person to buy health insurance, Clinton called it a tactic "right out of Karl Rove's playbook." In other words, it was something that Republicans would do to Democrats, not what Democrats should do to each other.

"It is not only wrong, it is undermining core Democratic principles," she said. "Since when do Democrats attack one another on universal health care?"

Clinton has long been skeptical of a single-payer plan, even though it's beloved by much of the progressive base.

"I have thought about this, as you might guess, for 15 years and I never seriously considered a single-payer system," she told The New York Times in a March 2008 interview.

Her argument against it was, in part, political. Selling such a plan would be hard because most Americans "become very nervous about socialized medicine," she said.

"They don’t really know that Medicare is a single-payer system," she added. "They don’t really think about that."

Also on HuffPost: