That's the last sentence of this NY Times article.
That sentence corroborates - as if further corroboration were needed - the existence of the so-called cost-shift.
The cost-shift occurs because the feds (and the states, in the case of Medicaid) do not reimburse medical service providers “all or substantially all of their costs.” Because the law does not require it. The government uses its market power not to negotiate fair reimbursements, but to dictate inadequate reimbursements for Medicaid. Same is true for Medicare.
As a result, the medical service providers naturally seek to make up what they can by increasing their charges to patients who can pay - patients who have better insurance than Medicaid or Medicare. That would be private insurance.
Unsurprisingly the feds' tactic to hold down federal insurance cost has the simultaneous effect of increasing private insurance cost. Since at least 1970, a parade of actuaries has rather consistently estimated this cost-shift from federal to private insurance adds something like 15% to the cost of private insurance.
By the way, the Times article also reminds us that when the subject is insurance and medical care, one should always read to the very end of the article. Important stuff is too often buried down there at the end.