It appears that you have some bogus info. Even if a death certificate says it, it is only as good as the person that gave it.I have found many many death certificates where the people didn't know the answer at the time so the next best thing was accepted.You run into this especially if the person lives to a very old age and the younger children in the family are left to give the answers. They just didn't know because they never knew the older generation.
Your Nancy Lynn married to William H Caruthers is the daughter of Elijah Lynn born abt 1810 and Mary born abt 1820 died 1899
You can easily find the family in the census papers.Elijah is mispelled as Elisha or some such thing a few times but you can match up the other members of the family.
There are clear census papers clear from 1840 though the years.
For proof I submit this will of Mary Lynn from Ancestry.com that clearly states the name of her daughter Nancy.
Ancestry.com Bedford Gazette; Bedford, Pennsylvania November 24, 1899
The will of Mrs. Mary Lynn, late of Broad Top township has been filed in the register’s office.Testatrix bequeaths a nominal sum to the heirs of her children, Abraham Lynn, Hettie House and Jacob Lynn, and gives to her son, Theophilus Lynn, $100.The balance of her personal property and real estate is to be equally divided among the following children:G.W. and Theophilus Lynn, Nancy Cruthers and Elizabeth Johnson.G. W. Lynn is named as executor.