I suspect that this is more nuanced.
There could be many explanations for your findings. From her working for a different stare or county. A different health board.
Her specific supervisory role may simply not be licenced, they aren't all.

Or she is indeed a bare faced liar.

By all means ask her.

Is it your mistrust of therapists in general that made you check on her or just a lack of trust in her?
I only ask as really that would colour what I would do next.