First off, I think you need to take a moment and remember that this is a 10 year old LITTLE GIRL you are talking about, not some skanky she-devil who is out to steal your sons innocence!
Some of these comments... good lord it is disturbing to think about how cruel some of you must be.
J., let me ask you a few questions:
You say you have set ground rules, you didn't say that this young girl has ignored them correct?
She invited your son to a FAMILY function, not some kind of one on on activity with just your son correct?
So what exactly has this poor child done that is so horrible? [I know you haven't said she's done anything horrible, it's some of these comments that just jump to trash a little kid...]
Do you remember what it was like to be that age & like a boy? I sure do, and I know that my intentions were nothing but innocent. It's already hard enough for kids to figure out these new feelings and emotions, don't make this little girl feel like she's doing something wrong just because she likes your son.
Give her a chance before you judge her. Call her parents, make sure they know what your rules and expectations are, and how about this - if you want a chance to feel out the situation a bit more, why not have your son invite her over for lunch or dinner? That way they get a chance to play & you can keep an eye on how things go, plus when you sit down to eat, you can take that time to get to know her better!