>>I know that my great-grandfather's first son was born on 2/14/1875 in Manistee according to his death record.<<
DC data is secondary source. Simply said, what you see on a DC is to the best recollection/memory/ and knowledge of the informant, and can be highly subjective in many cases.
The marriage record of the party should have the names of his parents. Marriage data is primary, the bride and groom state their parentage for the record. This is document you seek and get clues to confirm parentage.
Localize where the couple was married is done by using the census records. Figure out when and where they were married, find marriage record, find parents, work another generation back. These are the simple building blocks of all genealogy research.