Source?
Also, "socialized medicine" does not entail getting rid of the private sector, just regulating it. For instance, my GP runs a private practice, the only limitation is that she cannot set the price of an appointment. And if she was a hard-core free-market proponent of some kind, she could set her own prices freely, the only snag being that insurances would not cover her visits. Also, there is an argument to be made that doctors are veblen goods and that free price levels would not be optimal.