Some events are recalled by whether it was warm or cold, or whether there was snow on the ground, etc. While not as exact as a date, a time of the year may be helpful. Research in weather records assisted prosecutors in pinpointing what days in February of that year were unusually warm and validated the witness' testimony regarding the weather. I can't remember when my great- grandmother died, but I can remember being at the cemetery and standing in the cold. I can also remember my surprise when Mother said we didn't have to wear suits as it would be too cold at the cemetery.
Information given at stressful times is more likely to be incorrect.
A death is an emotional time and the informant may not recall details about the background of the individual as accurately as they might at other times. My great-uncle provided information for his brother's death certificate shortly after identifying the body at the morgue in the wee hours of the morning. Definitely not the best time to give accurate information. I was researching a Marie Williams who died in the Chicago area in the 1960s. A relative claimed to remember her death date.