"We need a public plan to keep the private plans honest."
But then why stop there? Eating is even more important than health care, so shouldn't we have government-run supermarkets "to keep the private ones honest"? After all, supermarkets clearly put profits ahead of feeding people. And we can't run around naked, so we should have government-run clothing stores to keep the private ones honest.
Supermarkets make money by selling people food. Clothing stores make money by selling people clothes. If they don't give people food/clothing, they don't get money.
Insurance companies, on the other hand, make money by selling people insurance -- and they make even more money by selling insurance, and then denying claims.
Surely even John Stossel can see the difference.