This is true; sight-reading is an extension of 'reading', and has its own challenges. For most purposes, reading, albeit slowly and methodically, would be enough to get the enormous benefit that it brings; sight reading becomes a 'must' when depping theatre pit shows, concerts or studio session work.
Many (most..?) concert pianists, and other performers, have the score in front of them, but have practised and rehearsed enough to not read from it, as it's been committed to memory. They have spent the time beforehand, though, studying the piece (reading it, obviously, but more than that, mostly...), and playing it through a number of times. Memorising is part of the skill in reading; few will be reading from the score 'live'.