The ITC faq (unofficial faq adopted by most tournaments, these days) rules that a psyker can only get one primaris free; that having powers from 2 schools (even if one is the forced primaris) means you aren't eligible for a second free primaris.
It is a gray area in the wording though, definitely! It comes down to consensus and how your local group does it, honestly, I think. Until the ITC faq ruled it out, I definitely played my daemons that way--just made sure to check in with my opponent to make sure they were ok with it before my matches, so when my ML1 Horrors suddenly had 3 psychic powers...
What sphinx of plascrete and adamantium bashed open their skulls and ate up their brains and imagination? Imperator! Imperator!