No worries.
We are humans, and many of us like to make assumptions.
My friend told me sometimes; that patients assumed she was a hospital porter.
She is a doctor with her ID displayed on her chest pocket--sad, but now she introduces herself as a doctor and directs the patients to the front office.
Life goes on, and the woman in your story possibly wanted to engage you in small talk.
Our world is getting better.
Well done.