Documents for benefits from divorced spouse

This relevant publication makes no mention of the requirement for a birth certificate :
http://www.ssa.gov/retire2/divspouse.htm

Here is a publication which provides guidance for abusive situations that may help :
http://www.ssa.gov/pubs/10093.html

You also may want to consider filing an appeal :
http://www.ssa.gov/pubs/10041.html