Editor's Note: (Steffie Woolhandler, M.D., MPH and David U. Himmelstein are both distinguished professors at The City University of New York's Hunter College, primary-care doctors in the South Bronx, and lecturers in medicine at Harvard Medical School. The views expressed in this commentary belong to the authors. View more opinion articles on CNN.)

(CNN) President Trump's critique of "Medicare-for-all" reform assaults the truth. Contrary to his claims, the single-payer bills in the House and Senate would upgrade coverage and broaden choice for seniors, along with the rest of Americans. And Medicare-for-all would slow the growth of medical costs, assuring Medicare's long-term financial health.

Steffie Woolhandler

David U. Himmelstein

Medicare currently leaves many seniors facing unaffordable medical bills. According to estimates from the Commonwealth Fund, the average enrollee spends $3,024 out of their own pockets on medical bills each year, and medical costs eat up more than 20% of total income for one in four seniors.

To escape some of those costs, many seniors are fleeing to private Medicare Advantage plans that restrict their enrollees to narrow networks of doctors, and often exclude cancer centers and other top-tier hospitals. But the trade-off might not be worth the savings, since the average person enrolled in a Medicare Advantage plan is still saddled with $2,472 in uncovered medical bills.

Medicare-for-all would plug these coverage holes, eliminating virtually all copayments, deductibles and uncovered services. It would also free seniors to choose any hospital and any doctor, and spare doctors from the managed care paperwork and restrictions on referrals imposed by Medicare Advantage plans, freeing up more time to spend with patients.

The President's claim that Medicare-for-all would break the bank rests on a study by the Mercatus Center, which receives funding from the conservative Koch brothers. But Trump leaves out the fact that even the Mercatus study concluded that a single-payer reform would actually reduce medical spending by $2 trillion over 10 years; the federal government's health spending would rise, but spending by employers, state and local government, and families would fall by an even larger amount.

The bottom line of the Mercatus study (which probably underestimates single payers' savings), and many others is that single-payer reform would lower costs for the vast majority -- including seniors -- and avert the funding crisis that looms over Medicare.

Medicare-for-all can upgrade coverage while lowering costs by cutting out the insurance middlemen who currently drain hundreds of billions annually from our health care system but add no value. This year alone, private health insurers' overhead -- the money they collect in premiums that goes for marketing, accounting, executives' bonuses, profits and more, instead of care -- will total $256.3 billion, 12% of their premiums. That's fivefold higher than the traditional Medicare program's 2% overhead, according to 2017 data.

And Medicare-for-all would shrink billing and paperwork costs for doctors and hospitals, which currently contend with the arcane billing, coverage and documentation requirements of hundreds of different insurance plans. In countries with single-payer programs like Canada (Canada's program is called Medicare) and Scotland, hospitals spend half as much as US hospitals, percentagewise, on administration. And according to research published in 2011, the average doctor in the United States was spending $89,975 each year dealing with insurance paperwork, $60,770 more than Canadian doctors spent under that nation's Medicare-for-all system.

Overall, a single-payer reform could save more than $500 billion annually on insurance overhead and providers' billing costs. In addition, our research shows that a Medicare-for-all program could use its market clout to bargain down drug prices to the levels in Canada and Europe, saving another $113 billion. The savings on bureaucracy and drug prices are more than enough to cover the nearly 29 million Americans uninsured in 2017, and improve the coverage for seniors and the tens of millions of others with unaffordable copayments and deductibles.

In his effort to tar Medicare-for-all as a socialist plot, the President invokes the example of Venezuela. But he ignores the successes of single-payer programs in capitalist countries like Canada, Australia, Scotland and much of Europe. The national health insurance programs in those nations cover everyone, cost half as much (per person) as our system, and get better results; US life expectancy, which used to lead the world, has stagnated and now lags years behind that of Canada and most of Europe. For what we're now spending, we could have a Rolls- Royce version of Canada's system.

The President's fear-mongering about waiting lists, bankrupt doctors and hospitals, and socialism mirrors rhetoric in the campaign to block Medicare in the mid-1960s. Back then, The Wall Street Journal warned about "patient pileups," and the American Medical Association mounted a campaign featuring Ronald Reagan that smeared Medicare as creeping socialism that would rob Americans' freedom.

But today, America's doctors are rallying to Medicare-for-all. Polls show that many doctors, and most Americans, favor such reform, and thousands have endorsed Physicians for a National Health Program's single-payer proposals. A 2018 poll from the Kaiser Family Foundation found six in 10 favor a national health care plan.

Ironically, the President claims the mantle of Medicare's protector, even as his chief economic adviser has announced plans for "entitlement reform" -- Washington-speak for cutting Medicare, Medicaid and Social Security. Meanwhile, Republicans continue to press for the repeal of the ACA's coverage expansions, and its pre-existing condition protections. While the sham replacement they offer would guarantee people with a pre-existing condition the right to buy coverage, insurers could refuse to pay bills for the condition.

President Trump's Medicare-for-all attack rests on fake facts and baseless smears. The insurance companies and drug firms whose profits would shrink under single payer will no doubt welcome his words. But the truth is that Medicare-for-all isn't just the best way to fix our broken health care system -- it's the only way.