Just to clarify: Who actually owned the dog in the first place, the guy or the woman? Sounds to me a bit like, he wanted to get rid, she didnt really, he made her get rid of it, she realises what a mistake it was to listen to him, and now wants the dog back.
Out of interest, what policy do most rescues have? Say you turn in your pet and you realise how stupid a decision this was, do you have a week or so that you can change your mind in? Like with human adoption, that the mother has a certain period in which she can get the child back?