Sharing Isn't as Simple as it Used to Be....What do you do?

This is more about parenting and less about teaching and education, and I want to hear your thoughts. 

When did sharing and playdates get so complicated?

I've recently found myself in situations where my 2 year old is playing with friends' children, and I disagree with how the other childrens' parents discipline (or don't discipline).  For example, Katie (she's mine) was playing with a puzzle and her friend just up and took the puzzle from her.  Katie, nonagressive as she is, just looked baffled and shocked.  The friend's mom looked at me and said, "X is the 3rd child; she has learned how to fend for herself and get what she wants."  I'm sorry, what?  If the shoe had been on the other foot, I would have insisted Katie return the puzzle to X, along with an apology.  So, what do you do in a situation like that?

What's worse, what if your own child starts acting noticeably different after a playdate with such a friend?  Katie is really good about saying please, thank you, waiting her turn, etc., but after playing with some of my friends' kids, she seems to "forget" how to do these things.  Granted, it is a temporary amnesia, but I don't like it (enough so that I have considered not allowing Katie to play with these kids on a regular basis).  [Yes, I know this sounds really over-the-top, so keep me in check here].

I guess the bottom line question is...is it OK to discipline someone else's kids?  I feel like it's not really my place to talk to other parents' kids about sharing, but I don't want to give my own daughter the impression that it's OK, either.  I think I can honestly say that I'd want the other parent to warmly, but sternly correct my child if she were the one who was not sharing/hitting, etc.  I'm not fooling myself into thinking Katie hasn't done some of these things on occasion; I just think I'm usually there to correct her on the spot.

As a teacher, I was able to be unbiased, so I could correct kids without thinking twice about it.  But now that it's my own child and someone else's, I'm stuck. 

Thanks for sharing! I'm dying to hear how you handle these situations!