Thanks for the reply, as always. 
When both are checked, they move at different speeds. When the scaling pivot option is unchecked, the small round pivot moves without affecting the geometry. However, whenever the scaling pivot is checked, the geometry moves with the pivot. The surface does not have construction history and it doesn’t matter if I cut and past it into a new file.
If I, however, start from scratch, the same thing doesn’t appear to happen. Also, even if I press “zero transform” and then duplicate the surface using the “duplicate object” tool, it gets seemingly non proportionally scaled by more than half of its original size. Luckily, I did manage to figure out that if I pulled an old Solidworks trick and used offset surface with a distance of 0.00, I got an identical surface and so far, that seems to have resolved it!
What can I say? Alias…
PS. I recently accidentally deleted all my preferences and had to transfer them again from my old OS X install, like I’ve done many times before. Only this time, whenever I launch 2013 I must manually make the shelf appear from the Windows menu, and I can no longer create curves using the “cv curve” tool, because they get locked in a -1 span setting, so I have to use edit point curves instead… I tried to go back to 2012, but that no longer allows me to save my settings and always complain about it when I try to exit the app.