The federal government controls the 67% of the healthcare system that compromises Medicare, Medicaid, the VA and a few other federal programs through funding, administration and management, any assertion otherwise is simply foolish.

"...that 67% of the funding doesn't equal 67% control of the entire system?" No 67% control equals control of the 67% of the system that the federal government funds, manages and administers.

So EZ, will you again call me a liar because your opinion of the definition of the word "control" does not seem to entail funding, management and administration of the several federal healthcare entitlement programs. 
Below are two of the federal agencies that wield the control:
The Centers for Medicare & Medicaid Services, an agency of the U.S. Department of Health and Human Services.
The Veterans Health Administration is America’s largest integrated health care system, providing care at 1,245 health care facilities, serving 9 million enrolled Veterans each year.