From the looks of it, for a companion to level up with the player character, the "PC Level Mult" checkbox needed to be checked (I guess this was the "bug" that made her stuck at level 5 or whatnot).
It seems as though checking "PC Level Mult" also checks "Autocalc Stats" and it greys it out so you can't uncheck the box. The result being that any modifications I made to her attributes and skills were reverted to their default values. The attribute boxes become greyed out so they can't be modified at all.
Bethesda's GECK wiki page on this says this about skills:
Skills: All the skills are autocalc'd if the box is checked. They can be changed after being autocalc'd.
However, after clicking on the skills area for about 15 minutes, I definitely concluded that I could not change them with the autocalc box checked. It would bring up an edit area for the numerical value, i'd type in a value and then the value wouldn't change. Is there a way to modify any of these values? From the looks of it, if I wanted to change Veronica into some cold-blooded sniper, she'll just end up as a sniper that can't hit her target ever since I can't modify her gun skill or perception (example).