I have a curiosity about this, so slightly highjacking.
If you were doing family geneology and learned say that you had recorded a birth date as Jan, 7 1896 because that was what was on the tombstone but later ran across a document that indicates a date of Jan 7, 1898, what would the impact be to your research? I'm asking because my as this is specific to a grandparent issue. The tombstone says one year but there is a census form someone else ran across that seems to show a handwritten 1908. There was lots of back and form within the family about which was right and maybe the tombstone was wrong or maybe it really says 08 but others think the handwritten 8 is really a 6. My opinion is who cares? One family geneolgist said that if the same woman was listed with different birth dates is could be confusing to future researches. I said I figured a future researcher would probably be able to couldn't figure out there wasn't 2 Bertha Eugene O'Mally born in the same small county within two years of to the same parents.
Well, if we just throw up our hands and say "who cares?" about details in genealogy, we might as well just go get a new hobby. Which is fine, because some people really don't "get" genealogy or why others find it interesting; some people like "family history" but prefer personality-based narratives rather than dated documents. So if that's the way someone views it, then no, there's no need to care about a detail like that. And I don't necessarily believe that those who compose obituaries have a "duty to the future" to make things detailed and accurate--as I said, they're often written in a rush as one more thing to check off the list during funeral preparations, and I know for a fact that some in my family have (accidentally) incorrect details in them.
Genealogy research can be pretty difficult sometimes. I had a long answer about the vagaries of different records, but I'll spare you guys.
Basically, I have a top 5 surname, which has always been a top 5 surname in the US, and ancestors who stayed in the same small geographic area surrounded by relatives (whom they married) and who were shockingly unoriginal in the names they gave their children. Plus official records like censuses, birth certificates, etc. are not 100% available or 100% accurate, mostly for very mundane reasons (not anyone trying to conceal anything).
In certain times and places people simply didn't find it important to remember the exact day/year something happened. Then you get an official insisting you put a date down, so you give it a try, and then by the time someone dies the official records are littered with four different birth years for them. Which is why I don't
find tombstones to be particularly accurate sources for birth dates--death dates, yes, because that event just happened. But the more time between when the record was made, and when the event in question happened, the more suspect it is, IME. Honestly I'd consider +/-2 years to be about par for the course and it wouldn't trouble me too much. More than that and I would start wondering if I'd gotten the wrong person. Also consider that much of the time I'm working on people who have passed out of living memory for everyone I know--all I know about them is what I find in records. So it would be easy to accidentally graft onto the family tree an entire incorrect branch if I didn't pay close attention to the details.
Who cares? Well, probably only other genealogies. I tell my mom, "No one cares if you dropped a stitch, Mom! It's a beautiful scarf, just keep going and don't unravel it to fix that one little thing." And she's like, "Well, *I* care." It's a hobby and people who like it, like to do it right, that's all.