It sounds like this individual does indeed have some trust issues. By virtue of making you aware of this she has let you in a bit to her trust zone. This is a compliment.

You have gotten many comments here about the recording being something that we would not do without the T's approval. That is also something that speaks of trust and openness. I think that she can be gently told, if you care to go there, that she might wish to discuss this with her T. You may encourage this.

In a gentle way the trust she has for you and your opinion may be helpful to the trust she is developing in therapy.

Just a random thought early this morn.