Why would
any company build a private blockchain? Private companies have top to bottom control of their systems, which means they don't need proof of work or proof of stake or any other system to establish trust: they can just issue PKI keys to employees from a database.
Private blockchain has never made any sense: you just give all your employees private keys and move on with your life.
EDIT: Which is to say, I'm sure a lot of people are saying they're doing it, and it is yet to be for anything more then to say "we're doing blockchain" to investors and the public.
EDIT 2: Reading through the Hyperledger case studies seems to bare this out as well - the implementations are comparatively small, and keep desperately asking the question "was blockchain vital to any of this, or was the actual innovation you just finally automated something into a database?"