There's a lot of misunderstanding of the adjective "private" in "private balcony." This term does not mean that other people cannot see onto the balcony. It means only that the balcony is accessible only from an adjoining cabin and thus is reserved for the exclusive use of that cabin's guests -- just like a private balcony on a condo development.
The fact that a balcony is not visible from other points on the same vessel does not mean that you won't be putting on a show for somebody elsewhere -- on a passing ship, in an apartment or office tower while entering or leaving port, etc. -- if you decide to use it for "private" activities. FWIW, "eye in the sky" satellites are producing photographs with phenomenal resolution, too -- so if you do decide to engage in "private" activities on a balcony, be sure to smile for the camera -- regardless of ship!
That said, if you want a balcony that can't be seen from other points on the same ship, the following Princess balconies meet that requirement.
>> All cabins with balconies except the aft suites and minisuites aboard MV Sun Princess, MV Dawn Princess, MV Sea Princess, MV Ocean Princess, MV Crown Princess, MV Regal Princess, or MV Royal Princess
All outside cabins on the Lido, Aloha, and Baja decks of MV Grand Princess, MV Golden Princess, or MV Star Princess
Have a great cruise.