I don't know where you get this. In my experience nobody who advocates for socialized healthcare is under this impression. They know how the system works, just don't think it's an efficient way to run it (it isn't).
The way the incentives are structured on the American healthcare system now are beyond ridiculous and having public published prices is a way to start a much needed debate about the underlying issues, with data and facts instead of political viewpoints.
It's absurd that having a baby in an average facility in the US "costs" five times more than a private hospital in Switzerland. I put quote marks on cost because that's usually billed price and insurance tend to negotiate down, so in reality is more like twice the cost, but still absurd at any level.