I think it depends. Have you got time to check it out yourself, maybe walk the girls back to their place and suss things out?
It would at least being easier if you could see with your own eyes? If you are happy with what the mums cousin has said (re stealing etc), maybe you need to be truthful with these kids and say I heard you can't play at xxx's house because you took things -is that true? If you do that here you will not be allowed to come back.

I had a rule that playing with kids at my house after school had to be arranged prior, not that day. Mainly cos I was working and my house was a total mess all the time and I couldn't bear the parents coming to pick up the kids and see it!

It's a really hard one - I've often been at the end of parents that can't be arsed with their own children - 3 times over the years I have come home to find small children in my house or backyard playing happily. 3 times I kept an eye on them or played with them to see how long it took for the parents to come looking and it was usually over an hour later.......no they weren't frantically looking for them btw because each time I could see their houses from where they lived.