No, it means you may potentially have all of those but there is no guarantee. Neither is there a guarantee that a publicly insured person wouldn't receive the same treatment. E.g. if there aren't any free "better/worse" rooms what are they supposed to do? Many of these are nowadays covered by employers as a benefit or for cheap (~5€) out of pocket if you want.

Private insurance matters most for specialists that don't (aren't allowed to) have (or want) a public insurance license.