I dont' know what she was specifically referring to here with regards to your real family as she put it. And without knowing if something else has been going on long term it's hard to say. Clearly it was off the cuff and she was reacting to something but only you can know what that possibly could be.

Do you have an ex, other children, etc that you have to remain in contact with? The only thing I can see this as referring to is that she feels as though you're playing at being a family and she feels in competition with that. It may be something that she feels a lot of the time and in this emotional moment (thinking about the well being of her child) she may have just blurted that out without thinking.

all conjecture of course as I don't know the real details, I'm only assuming what it seems to mean.

Whether people take this as an offensive statement or not, the reality is that it's a sign that something that you were unaware of here is going on.