I am not comprehending what the problem is. If there is a birth certificate for the child, it would state the parent's names, except in strange cases. THAT, establishes the relationship, so why would you want a separate FACT where the source-citation would be the same as for birth?
So that leaves cases where there is no found birth certificate, which is many people. So it came from some other source--a will, a book, etc. I still would list that as the source for the FACT that there was a BIRTH (usually would not have a date--still, there was a birth).
Can you please give me an example where the BIRTH fact cannot carry the source telling you that a birth occurred and who at least one of the parent's was?
Or are you talking about relationships other than parent-child?