The Stargazer scene made some sense when paired with all versions of the original endings in which it was implied that galactic civilization had collapsed. It doesn't make any sense at all when paired with the Extended Cut endings (except Refuse), and is best ignored as a non-canon tribute to space exploration.
I saw it as a wink at the fact that we all played Mass Effect a little differently, though that runs into a similar problem - the differences between playthroughs *are* big enough that they wouldn't be lost or obscured over time. To name an easy example, the fleets faced down the Reapers at Earth with the assistance of either the quarians, the geth, or both. With electronic record-keeping, something as simple as which species were there for the final battle would not just be lost or forgotten. Maybe not everyone would have all the facts at the tips of their tongues (maybe the stargazer cut his Galactic History class that day), but they'd still be able to look them up somewhere. Even details like individual mission reports would probably still be in an archive somewhere that military historians could study.
That's not to say absolutely *everything* would be preserved, unless the Normandy's security systems and/or people's omnitools are in some sort of constant "record and archive" mode, but all of Shepard's "big decisions" would probably be known facts unless someone actively covered up details.