This is reasonable, I can't just take your word for it that you can cure baldness and give the head of an important person into your hands without a safe inspection and verification.
Initially, Auburnli trusted you because all the feedback from the students below was positive, and she had stealthily visited with her identity concealed, gaining trust from both Ange and Negris at the time.
Otherwise, with her identity as the Death Star, any healing method would have to be repeatedly checked and verified before it could be used on her.
However, Negris's first response was, "Doesn't that mean Little Sapling will need to be examined? That won't do."
Anthony added, "Yes, I also think it won't do. What if it gets bumped or scratched, that would be trouble. And for us from the Church of Light to offer the Tree of Life, what does that mean? It's like telling them that the God of Light can't solve baldness, but the God of Life can."