This bug report is about two site settings (under "Site options -> General settings")
1. Allow public pages
2. Allow public profiles
Currently, the behavior of these is tied together. If "Allow public pages" is turned on, it forces "Allow public profiles" to be on. If "Allow public pages" is turned off, then and only then, the admin can toggle "Allow public profiles" separately. As of Bug 814328, this behavior is reflected with Javascript that grays out "Allow public profiles" when it is being overridden.
However, there's no ironclad reason why these two settings have to be tied together like this. There is at least one case on the forums, of a user wanting to allow public pages but *not* public profiles: https://mahara.org/interaction/forum/topic.php?id=6431&post=27235
Frankly, I think the reason these are tied together in the first place is a bug, not a feature.