I agree that it may not have been the daycare provider. You can ask if it was, but it may have been the offended child, or another child in the room. Both of my kids have been in daycare facilities since they were babies, and in every room after the children are verbal, there was always at least one child who would come and report every thing my child did that day that wasn't to his/her liking. Teachers and daycare centers try to keep things confidential, but I try to take comfort in the fact that I would rather know too much than have a child abused and not be told by anyone.
It's the other parent who needs to be spoken with by the center, if the center did not reveal the information. That was an inappropriate way to respond. I feel sorry for the parent and their child. I hope they don't believe that they will be able to follow their child through elementary, jr. high and high school and contacting other parents about every small thing that happens.
(By the way, when my son was 2,he got hit by a flying car in the face, and ended up getting stitches the night before we flew cross-country for my brother's wedding that he was in, and I don't hold it against the child or parent. These things happen....)