It all depends on whether or not a given shot was subject to being put through the optical printer. Sometimes, all it needs is addition of a title card or credits.
That is correct.
On my third or so go round of season 1 & 2 on Blu-ray I took out my note pad and jotted down the number of new 'viewscreen shots', 'space shots', 'fixed shots', new matte paintings & lastly,
'degraded shots'----that is, shots where, for whatever reason had lower quality that the main portion of the episode.
The reasons for the degraded shots are--------
Title cards/credits being superimposed
dissolve shots where one scene fades into another
beaming in shots
phaser shots
fade outs & fade ins before and after the where the commercial break went.
shots that were 'zoomed' in editing----that is long shots turned into medium shot and medium shots turned into close-ups.
A prime example of this is in Return to tomorrow in the chamber where Sargon first takes over Kirk. All the shots of Shatner being taken over with the globe in the foreground left were zoomed in causing the grain to become much obvious (because it's enlarged like the rest of the pictue.)
The absolute hands down worst example of this is in 'Changling' where Nomad is emerging from Dr McCoy's office after attacking Chapel. They had apparently forgotten to get a shot of Nomad leaving the office and the instead used a repeat shot of Nomad leaving the turbo-lift. They zoomed it in close horribly to obscure the fact he is actually leaving a turbo-lift. (you can still see though that swirly design thing in the back of the lift) It is the most terribly grainy shot in the entire first two seasons of TOS. It is so bad in fact that they should have replaced it with CGI for the 'Enhanced effects' versions---the way they fixed a few other live action shots.
If your Blu-ray player has a 'zoom' function, simply take what you consider a perfect, pristine shot and zoom it 2x----you will imediately see the grain become much more apparent.
In all of these cases, the remaster crew could not fix these things because (unlike dirt, scratches, fibers, tears & warps) they were there in the first place from the first editing.