All too often, people use others to try and voice their feelings without a willingness to own up to them. This woman is saying that her daughter says these things is probably in truth, her feelings. It sounds like you've spent a significant amount of time with this child. Do the mom's comments sound like something the daughter would say? I suspect not. I would take the opportunity to ask the child if she likes playing with your DD, if there are any problems etc and see what she says.
Unfortunately, it may be another case of simple jealousy. As your daughter gets older, she will outdistance the other girl. Many parents feel inadequate with their parenting when faced with a child that knows so much more, so much younger. It's stupid but it's very real.
