Medicare is about 1/6 of US healthcare spending so it obviously isn't subsidizing private payers, even if you make a ridiculous assumption like 100% of payments are fraudulent.
And then in reality fraud rates seem to be quite low, at most a few percentage points of overall Medicare spending.
What I meant by fraud, was not cases of outright fraud where someone bills Medicare for services never performed, although I'm sure that happens all the time.
I meant cases like the late night commercials "call now and get a free motor scooter! Just fill out a simple form and we will bill Medicare."
And more relevant are the cases where hospitals bill medicare huge amounts for long patient stays. Medicare always pays what they are billed, after all it's the government paying, they just write a check.
Meanwhile if you bill an insurance company they will negotiate, argue, refuse to pay, deny coverage, etc. If you bill an uninsured person they can also just decide not to pay in favor of paying more important bills like food and shelter.
So, the hospital is actually fine with this, they simply write off the unpaid amount on their taxes as a charitable expense, and increase rates, which Medicare will pay.
So, as you can see, Medicare (plus tax breaks) create a situation where the government subsidizes and distorts everyone else's health care costs.
And then in reality fraud rates seem to be quite low, at most a few percentage points of overall Medicare spending.