I would need to confront her. And how she responds, beyond the factual information, would also be valuable in coming to a decision about her trustworthiness. It is generally an ethical violation to misrepresent one's credentials or scope of authority. My state also has a very specific designation of those who are certified as supervisors, a credential which follows degree conferred and is earned through a combination of testing and years of practice. It is determined by the State Board of Examiners.

I do believe that your investigating her background is in no way a breaking of trust: any misrepresentation of herself as a professional would be her breaking of trust.