You mean unannounced channels?

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No it doesn't. Even Super Testnet doesn't agree with it being called "private" that it's a misnomer.

Ironically it also removes plausible deniability

In your own link:

"An alternative name is private channels, but there’s contention between experts about whether the channels improve privacy or not, so it may be preferable to use the universally accepted name “unannounced channels.""

If YOU cannot see, then is private. Deal with it.

Exactly. It might be private from ME. It's not private from your counterparty or interested third parties. Cope.

"“We call private channels 'private' but they are really not, they are more like unannounced channels,” Giorgio said, adding that there are currently ways to exploit the Lightning Network that enable a node to discover an unannounced private channel."

"Unannounced channels are not readily discoverable and cannot be used for routing payments by other nodes. However, their existence may still be inferable through blockchain analysis or routing hints in invoices."

"If you opened an unannounced channel and never created an invoice, it’s still possible your channel partner revealed the channel and public key anyways. They could have included it in one of their invoices. They do not need your consent to do this."

https://21ideas.org/en/lightning-network-privacy/#private-channels-are-not-private

https://bitcoinmagazine.com/technical/state-of-bitcoin-lightning-network-privacy

https://massmux.org/i/151883354/privacy-considerations