I think that death records are the least reliable of all records. Often,
the information is given by a person who is the least distressed and
with the least accurate information at the time of the death. Of a
husband and wife, the spouse who dies first has a much better chance of
having a certificate with the correct information because the other
spouse, who knows the information, is alive and available for
questioning. When the second spouse dies, all bets are off. An in law,
neighbor or grandchild could have provided the information and just got
it all mixed up with other family information.
In my family I have a similar situation. In marriage records >from the
1870s, the mother is listed as Sarlotta Kanitz Back. But when she died
(and she died second) all of a sudden she's Sarlotta Epstein.
So, I'd go with the birth certificate and try to find more corroborating