Garnet could be viewed as a Red mage with the logic that Psi has presented. Not offically by name , but through her abilitys maybe.

Dagger had offencive summons, and low leval white magic (not that she was a crippled at w.magic but she was not a pro either. I Know she didnt have a sword, but she she was more usful for attack then healing. And on the magic front, beat Vivi as well as on the psychical attack front. So Its fair to assume she was a red mage at least in spirit. After all she had white magic (limited) and Summons (which acted like elemental attacks) which could be concidered supierior black magic, as you could power them up, they could not be reflected, and you did not need Stiener to cast the ulimate spell without harming your party.

The ironic thing is even Dagge's trace lends it self to attacking with elemnts, where as Viv's only alows you to double cast. In short Garnet is better at black magic and attack then Vivi. She is better used in the game as a red mage then using Vivi in for your elemnet spells if you leval her up right

Eiko was more of a real white mage with summons, but would not be concidered a red mage as her summons where not all element based.

So yes your Thoery works for me