So both assumptions are flawed. Medicare does not pay as much as private insurance, because it doesn't negotiate rates (it sets them). So you either accept medicare, and get the medicare rates, or you don't take medicare.
And medicare pays on average are bout ~70-80% of private insurace (at least according to my 5 second google search).
So, Bernie's study used an artificially low number (60% instead of 80%), and the assumption by this article is artificially high (100%, instead of 80%).
Funny thing, if you use the actual 80% number you end up spending....pretty much exactly what we do now.