On the whole I think things are best left, unless your dd has asked for your imput. Even then, go in with care. We had an awful situation which seemed to escalate and I found myself wishing I hadn't got involved.
I am friends with a woman but our two ds's don't really see eye to eye. They will play together when we visit each other but don't tend to when they are at school. Generally I would say not to get involved with your kids' when they fall out with their friends. They will work it out for themselves. I only step in if things get nasty.
I don't think you should force your dd to play with someone if they really don't want to. And I feel it would be unfair of your friend to expect it too. Can you have a word with your friend? Would she be approachable in this way?
I tend not to get involved in the children's friendships (even if I don't like the friends). I find that they tend to sort themselves out in the end. They change the friends that they play with so often. Also, I think that they only rebel against us if we try to force their friendship choices.
Maybe she lied cos she thought you might be upset that your friend is your friend but that things aren't quite so rosy with her and the dd?