People lied about their age on a regular basis in the past. My maternal grandmother did so early in her career, and my paternal grandfather's year of birth was given incorrectly on numerous occassions. Cite all of your sources and be done with it.
There are some records which are more trustworthy than others. If you have an actual official death certificate for the actual deceased, use that for the date of death. Otherwise, if it is just a name listed on the document (date of parent's birth, for example), use that as the starting point for a brand new search and go find original records.
But always, list all your sources.