Chances are the information in great-great-grandpa's death certificate and obituary were provided by the same person. This means that the fact they agree with other does not make them any more "right." Getting records where there were probably different informants as to the same details increases the chance you get the "right" answer.
And sometimes no one knew the right answer. But relying on one source or several sources made at the same time from information probably provided by the same person may send your searches astray.