This sounds a bit odd to me - if he was the childs childminder then it would be part of his role to change her clothes as required rather than get a complete stranger to do it. It's not as if people in the park would think anything, they would presume that he was her father.
I agree though that it is sad that people have to feel that way around kids even though they are perfectly innocent. However, since I have had my own children, I do feel suspicious of other people who have contact with them. This is probably heightened by my other halves former occupations as both a mental health nurse dealing with people who have been abused as children and have then abused others and he then worked doing Criminal record checks for people who work with children.
A lot of people take these checks as comfort, but all they really prove is that someone has not been caught doing anything. They also, at present, do not have to be completed by anyone already operating in a position where new people would require to be checked. e.g sports coaches and scout leaders etc.
It is sometimes a very sad world we live in, and child protection is paramount in most parents minds.