This is only the beginning for you..
First of all, I don't understand why coming from a disadvantaged home would make a difference, However, the different methods of parenting and values taught can make a difference.
My 14 yr old has gone through several friendships that we were not crazy about. Most of the time we keep our mouth shut and lets things work out for themselves. It is like 2 rough stones....they rub together long enough, things smooth out.
I have said no to some get togethers, especially around age 10 and up. We had 1 girl (middle school) that would have lived here if we let her. In the beginning, I treated her a couple of times to the club, movies or something like that. THEN, I started noticing a pattern for requests to do things like shopping, movies, Starbucks, etc that she wanted me to fund. I have NO problem doing that if someone is genuine and appreciative. We did sort of take this girl in because she was and is in an unhappy home and if she had 2 nights a week at our house that was peaceful and fun, then maybe she was more relaxed and unstressed when she did get back to her house. In the end, I did feel like I was taken advantage of but I would do this again for the right reasons.
Now my daughter has never given me a problem when I said no to someone comong over, even elementary school. The reason is because even in elementary school things started missing from her room. We've ended up at other girls homes, speaking with mom (not a fun thing to do) to retrieve my daughters nice clothing, dresses, Ipod and Camera. Who knows what we are still missing and not noticed. It is sad when you figure out who is doing these things.
If your gut tells you to not let your daughter go play...then follow your gut. You know what is best. Is there an option for the little girl to be at your home or is there that much dislike for her?
That said....I've had girls calling to come here, etc. for the wrong reasons and have simply said "we have other plans". Continue to have "other plans" or something going on. DON'T feel obligated to include others into your plan. My daughter is old enough now to weed most of the bad apples out and she does a good job. However it was a learning experience for both of us.
I know we are not finished on this road of friendships but it is much better and her friends now are good friends. It is hard being a good mom and not being judgemental sometimes. My advice is keep all lines of communication open with your daughter. Don't talk badly of others because it will come back at you. Do talk about behaviors and what is acceptable.
Good luck to you.