I was worried that her dad might be worrying about this - it looks as though she jumped on it before he could read it - you can see she has provided a link to the article in the text before.
I think the tone of the message from her dad, the fact she is denying it probably as best as she can in 140 characters, as well as using the words "for future reference", plus I'm pretty sure I am right about Dougals tweet, gives you a good indication of where they are at currently.
I don't really know why she made that grocery shopping photo hidden from her profile, I can't remember the exact timeline but if she did it before the article came out saying Drew posted a photo of her perhaps she was trying to hide it from her friends for now but now the article has outted them.