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.
In fact Diyonisius Exiguus made some errors when counting back to establish the anno Domini date system and as such Jesus would likely have been born between 4 and 8 BC.
No need to fuss about calendars. Just need to revisit Dr. Macdonald’s Temporal Mechanics 101.
There have been several temporal incursions since the DS9 crew did theirs - Voyager, Picard, SNW and Prodigy, not to mention the rippling effects of the Temporal Wars established in Enterprise and Discovery.
Dates and details can slip as long as the major events stay more or less the same.
The Cage, the original pilot, was filmed and screened in 1965. It was reworked into "Menagerie", which contained a lot of the original footage, but aired in 1966.
So you're saying the original timeline, well call it the Pike Prime timeline, is the real timeline, and that the show containing Kirk & Co, and everything from 66 onward, is fiction.
You can see now that some people are trying to establish their own realities as truth, ie changing facts, rewriting history, etc. What's to say a certain set of assholes gained power, rewrote the archives for their own purposes, and those archives are what survived WWII?