Even the JR group in Japan does not build the lines themselves. The actual infrastructure is built by the JRTT, which is a state agency. It's complicated becaus

Even the JR group in Japan does not build the lines themselves. The actual infrastructure is built by the JRTT, which is a state agency. It's complicated because JRTT owns many companies of the JR Group and is a shareholder in others so one may get the impression the JR group is building the infrastructure, which it's not. The JR group itself is only profitable because the Japanese government took on the vast majority of the debt from actually building the infrastructure. So no, the JR Group is not a counterexample. It's still unable to actually build infrastructure without government power despite having inherited so much of it, and it's not able to profitably pay off that infrastructure which is instead paid by the government.