I agree with you there's no evidence. But what is interesting is that on either sides of Meena, there are 6 brain cases like the one that supposedly received Nara's brain. It is not far fetched to assume that they received the brains of the volunteers who gave their body to allow Meena to learn biology or medicine. The Institution obviously developed a brain transplantation process and we can assume they did not develop it just for the Director, but also to allow to provide a new body to these six brains.
Or maybe these brains were put in robots used at teachers in the school, which would explain why it was "easy" for Sawatari to do so with Nara.
Obviously, it's just speculation at this point.