The counterargument to "words mean what people agree they mean" is that "to computers, instructions mean what they have already been defined to mean". If you change Python's meanings, you need to tell everybody that you're using Python 3.5-Joe, not Python 3.5.
Clearly true, but in this field "private" is really being used to denote "not a Public Blockchain like Bitcoin and Ethereum".
It doesn't mean "actually private". It means "we built our own rather than pay to use Ethereum".
Private really means what you think it is "a blockchain that only a small selected group can access". A lot of "Private blockchains" are just Ethereum-nodes running behind a firewall and with a secret genesis-block.
It does not, however, mean that it cannot be peer-reviewed. Allthough that still leaves the problem of not knowing if what you've reviewed is what is running.