You didn't ask, but if the lady you interacted with is going to be your supervisor, do not be hesitant in your dealings with her. She will be very sensitive to what she perceives as honesty vs. dishonesty. Always state your facts very clearly with her, as she has already identified this as an area she believes some people have problems with. It seems that her level of trust is probably different from yours due to events she may not have dealt with fully.
JMO, and because I want you to have a great career experience.
We all have scars and quirks from very hurtful life events. I'm not judging in any way, just giving a suggestion to increase the comfort level in the workplace.
Maria