Calling Japan Rail privatized is a "ehhh, kinda, in some places, if you squint" kinda thing.
Technically, yes, the JR's are private companies.
But track construction is generally done by a government construction company financed with Japanese sovereign debt. The completed tracks are then long-term leased to the JR's at favorable rates.
Is it really a private company if the key capital outlay is done by the government and given to you with a sweetheart deal? ehhhhhh.... you can call the operator company private, but you're being dishonest if you call the system privatized.