As a parent, you are always right to be concerned over your child's safety. At her age, it is easy for someone to convince her that what they are doing is ok, especially someone she trusts like a friend.
I would first advise that you make sure you teach your daughter that anyone touching her is wrong. When my son was that little, I taught him that no one should see his underwear except his doctor, Mommy, Daddy, and who ever else I trusted. Basically, if you wouldn't let them change your baby's diaper, they should not see your child's underwear. My son is now nine and shy about changing clothes in front of other people, but he has always been safe.
I had a major concern with this area to cause me to think about this. My brother in law's kids were harmed while his ex-wife was still a custodial parent. Its sad to fear your own child's cousins could harm him, but who else can he count on to keep him safe.
As for your friend's child, it could be many things. At ten years old, he may have heard things from kids at school and be curious or it could be that someone your friend trusted violated that trust. I have also heard of kids being curious after accidently seeing into their parents' bedroom. Or, this could be as innocent as the boy watching adults with babies and considers her to be one as well. He may just be trying to prove he can be a grown up and help her when she was crying.
When you take her to the pediatrician, you can ask the doctor to check to see if anything has happened to her. They can do this with an external exam that won't be any different than a diaper change and you can be present as well. Just explain what you have said here and that you don't know if the boy is just playing or if you should be concerned. You shouldn't have to give the child's name unless there is proof she has been assaulted. If she has, then upsetting your friend won't be as big of an issue. If she hasn't, I would recommend a way of teaching her that her underwear area is special and only the people you tell her can see it and only for doctor's appointments or cleaning her. But either way, I would keep her in your sight just in case for her safety and your peace of mind.
No, you're not overreacting.
Keep your child in your visual field when your best friend and her son are together with you.
I adore my former best friend (the years have separated us) but I can't believe, in retrospect, how I nearly allowed her child to try to blind and harm my children.
This 10 year old's behavior isn't typical. If you lose your friend because of it, well, okay.