Normally I would agree with you but in the case of my wife's grandfather and great-grandmother, the information about parentage on their marriage records (two each) was not correct. In fact, both told fibs all the way through their lives, on marriage records, censuses, military service records, etc. The only accurate information about great-gramma's parentage was on her death information which was given by a nephew, a son of one of her sisters. Both of her sisters, by the way, did offer the correct information about their parents on their own marriage records.
Grandpa, perhaps because he was illegitimate, rarely gave the correct information about his parentage. Information about his parents on his death record, unfortunately, was wrong as well. I think this was because the informant, my wife's mother, was never told the entire truth about her father's family. She took the erroneous information from her father's marriage record.
The lesson here is never completely trust any record, but look for many different sources in order to determine what might be the real truth about relationships.
I think that is wrong information by her widower. When there is a conflict between information on a marriage and information on the death certificate, I tend to believe the marriage because in that case the person is alive to provide the information, whereas with a death certificate the information is only as good as what the informant thinks he knows.