The woman tells me stuff unbidden - but I have no idea if it is true or not. I mean she could say her favorite color is blue - but it could really be red and she just made something up. (I don't know or care about her favorite color - it is just an example). For me, it makes no difference about the therapist and her personal stuff at all - and I think she lies about most things she says.
So while she does not act particularly secretive, her acting does not mean she is not.