I read a psak about a man in Israel who was divorcing his wife and didnt want to pay child support. He claimed the kids were not his.
So they took a DNA test (There were 2 kids) and the DNA showed that one kid was his and the other not. He was still ordered by the Rabbanut to pay child support and the daughter was not a mamzer. (It was the daughter who was not his daughter)
other cases involved conservative or reform weddings and remarriages where the Rabbanut delcared the original wedding invalid to avoid a mamzer
The point is time and time again Rabbanut try to avoid having someone become a mamzer even if there is strong evidence to prove so (ie they claim the original wedding was invalid)
If it came down to a case where there was an actual person involved who might be a mamzer, I suspect the rabbanut would find a way around it even if Rav Elishiv held differently