My headcanon is that after world war 3 we lost track of time (for a while; survival was priority) and a lot of records were destroyed / reconstructed, so the dates become fuzzy after world war 3, and by the time of TNG and DS9 those fuzzy dates had become accepted as fact because they didn't know any better. The eugenics wars haven't happened on the canon dates, but whose to say they don't actually happen 10 or 20 years from now? 😛
Real life example, our date system involves numbering based on the birth of somebody that almost certainly didn't exist. It's just widely accepted that Christ was born 2024 years ago. Or would it be 2025 years ago? I'm too tired to figure that out.
