@jespah,
Unfortunately I don't know this cousin so well. They have lived across the country from us. We only see each other once every so many years. She seems very sweet but what I know for sure is she suffers from anxiety, has some medical issues, has gone haphazardly to college, and has lost her most recent job.
So no real structure - that is really the only facts I can give (trying to be objective here).
I can surmise - and I realize this is totally surmising... she has difficulty with her parents - she is the youngest and - only one still at home it seems they have her do a lot for them. I know they are fairly strict so I think this could be influencing her on suggesting that my daughter can leave at 16. That is the only reason I would think she would say that.
I only found out about this after I got home from work last night - after my husband had spoken with my daughter for quite a while. It seems the talk in the end went well. He pointed out how this cousin although having anxiety is not an expert in the subject and not a doctor. He pointed out sort of like you are saying look at her cousin in a critical eye - what her cousin is going through and how she may not be the best person to go to for advice. As well as suggested who would be better to go to for advice and why.
I was really surprised (and initially PO'd) that she said something along the lines to her that she could move out legally at 16. It isn't like we are abusing our daughter and she is across country so how could she even know how things are? I just cannot even imagine suggesting a teen a move out from their parents.