Ok, the issue was the permissions on privacy.php files... (I think). It makes me really sad when I can see that even if I figured out what the problem was and fixed it (well, sorta), I still remain utterly clueless what all the error messages meant.

So now I deleted all text from Admin > Define > Privacy Page. It's all gone.

Then I added some text to the [ define('TEXT_INFORMATION', 'Your Privacy Notice should be on this page.');] part of the "privacy.php" file in custom template folder.

And nothing on privacy page except the "back" button. Where did I go wrong?!