That's a pretty far stretch considering four hundred Enterprise crew members all knew what happened and where Khan was ditched.
Maybe they erased everything? Maps, log entries. But you still have the human factor.
Why should anyone except the people we know met Khan have any idea what happened and where Khan ended up? And in fact, most of
them wouldn't have been told (ie. the yeoman setting the table at the formal dinner or the miscellaneous other crew who only saw Khan briefly).
It's not like Kirk would have broadcast his log entries to everyone as part of any "Good Morning Enterprise" briefings.
Most of the crew probably never even saw Khan, and wouldn't have been told what happened to him.
Getting back to the thread topic, it's an interesting issue, but rather unrelated to the above, that Chekov doesn't appear to realize at first that Ceti Alpha equals Khan. The three interpretations are clear, choosing between them less so:
1) Chekov doesn't remember that Ceti Alpha is where they marooned Khan.
2) Chekov doesn't know that Ceti Alpha is where they marooned Khan.
3) Chekov thinks that being on Ceti Alpha VI is sufficient reason not to worry about Khan, who is stuck on Ceti Alpha V and probably dead anyway.
It's easy to plead #1 because our heroes get around - Khan is just a forgettable adventure among hundreds, and his place of exile a mere name and a number among tens of thousands. But then we have to consider why Chekov hasn't refreshed his memory on the topic of the star system they are approaching. And there we have to decide whether Khan has been omitted/erased from records, or whether Chekov simply doesn't give a damn about records. The former is IMHO likelier, because Chekov was raised by Spock who always gives the obligatory exposition about the target planet at this stage of an adventure.
It's not difficult to plead #2, either. We didn't see Chekov in "Space Seed". He was probably aboard because Khan claims to remember his face and even correctly associates it with his name; stardates would have us believe he came aboard for "Catspaw" at the very latest, 130 SDs (probably a month and a half) before Khan. But he wasn't the navigator on duty when Khan's ship was found, and it's possible he wasn't the navigator on duty when Khan was marooned, either. And Kirk never tells his crew where the ship is going or what she's doing.
Dramatically, #3 is the least satisfactory - Chekov's surprise appears far too complete, his dawning recognition of the name Botany Bay at odds with the idea that he would rapidly shift mental gears from "Khan is over there" to "Eek, Khan is here!".
Timo Saloniemi
First: Chekov was "raised" by Spock? Whut?
Mentored? Yes. Taught? Definitely. But raised? I kinda doubt that. Chekov has family in Russia, on Earth.
Second: Of the three possibilities mentioned above, I don't see a problem with combining them.
As a very junior ensign, Chekov wasn't a Bridge officer at the time of "Space Seed." It's been speculated that he might have among the Engineering crew (offscreen), so that's how Khan would know his face. Or maybe Khan just decided to review the crew roster, along with the technical manuals when he was recuperating in Sickbay.
As a very junior officer, Chekov wouldn't have been told what happened to Khan. Why would he? When dealing with issues dangerous enough to merit being classified or hushed up otherwise, the last thing Kirk would have done would have been to let all 432 people on the crew know what happened to Khan and where he and his followers were marooned. Chekov wasn't told
at the time because he didn't have the clearance to know, and he didn't have the need to know.
All that said, many years later Chekov worked his way up the ranks to the First Officer's job on the Reliant. That puts him within one step of the Captaincy, and at some point he could have been told about Khan, or found out somehow. The confusion over Ceti Alpha V and VI is logical if they're twin planets (or were), and thus Chekov's reaction could very well indicate that his memory of Khan (whatever he might have witnessed, been told, or found out later) was triggered by the words "Botany Bay" and the sudden realization that "THIS is where they ended up? Ohdamnwe'resoscrewed!" becomes entirely reasonable.