As I understand it : ( and I have submitted a sample which did tie me to distant cousins that I was unaware of .)
The paternal test only includes the direct paternal line , father , grandfather ( not grandmother ) , great grandfather ( not great-grandmother ) , etc.
Mitocondrial DNA is just the opposite , mother , grandmother ( not grandfather ) etc.
So at the grandparent level only 50% of the grandparents are represented ( 50% are not ) . At the great grandparent level , only 25% of the lineage is represented ( 75 % are not ) , at the great – great parental level , only 0.5^3 or 12.5 % ( 87.5% are not ) ,etc.
She would win the case in court .
However , if someone has done genealogy ( such as LDS ) and their tree has a common ancestor which is in some organization’s data bank , that organization can make an inferred match to that common ancestor . In that way , the family tree starts to fill out again .