Your interpretation of "private" as in private assets is understandable.
But it isn't the kind of private we talk about.

Private assets means its an asset that cannot be sold to anyone or traded among anyone, that isn't allowed to do so by the asset issuer.
A private asset issuer himself determines who is allowed to trade in those assets and the protocol simply denies anyone who is not on the "allowed" list to receive that asset or even place a buy order.

See this link for when I first introduced the concept (includes some more business oriented views on the matter from our project lead)
https://nxtforum.org/asset-exchange/private-assets-for-use-in-financial-institutions/