Not necessarily true. Governments can run well. The European social democracies are a model of what would be considered "large government" in the US, but they are effective. The right wing Libertarian Cato Institute even rates Denmark as the best place to do business in the world..
Government-run systems, as with other monopolies, largely function poorly. But they just have to be better than a poorly-functioning market.
As I showed earlier in the thread, the administration in government single payer systems is a lot better than private for profit companies. Turns out there isn't much overhead in sending the bills in to a single place, then paying the bills. It's efficient.