Just got the vial @ KoS with a Erudite Prexus Enchanter. Used a lvl 3 DE mage persona to run through (not needed) and Reania would not give me the vial saying something like my skills were not advanced enough (guessing there is a lvl component). Personaed right back to ench behind her, said the phase and got the vial. Tried one more time while she was facing me just to test and when I said the phrase she responded with the correct phrase (though they are lore so I didn't get an additional).
tldr no faction needed on Teek?