>>(Medicare and such) had only 2% overhead cost.

I have heard the same - very very low overhead, and it does not quite ring true.
I did some work for a bureaucracy, and they were proud that they only consumed 20% as they passed the money from one layer of government to the next layer.

However, even if somehow this is actually an efficient government program, Medicare is easier to defraud than private insurers precisely because it is good at spending money with so little human attention.