Or else they just consciously decided to change it.
It's possible. On the one hand, the script was by Maurice Hurley, who was the showrunner and (at the time) apparently on pretty good terms with Roddenberry and his lawyer (the widely detested) Leonard Maizlish, so it's possible that the script reflected a revised preference by those "at the top" about the show's chronological setting, reached subsequent to the drafting of the Writer's Guide a year earlier (which in reality had been written mostly by David Gerrold and not Roddenberry anyway).
On the other hand, it's kind of odd to have something that was subsequently so pivotal slipped in so casually, and I'm honestly inclined to believe that it may well have been just an arbitrary date inserted in the first-draft script, which then wound up being used as the shooting script because it couldn't be revised due to the 1988 writer's strike.
I do recall reading that when the first edition of the
Star Trek Chronology was in the works it was Roddenberry's assistant Richard Arnold who was the primary figure insisting to the Okudas that the events of TOS had to be set exactly 300 years after their broadcast date. Arnold wasn't really involved with the show in S1, so the date in the script couldn't have come from him initially... but whether his later insistence arose from his own interpretation of the "2364" date, or whether it genuinely reflected Roddenberry's own preference, is anybody's guess.
Ultimately, it could've been deliberate, or it could have been completely arbitrary, and we have no way of knowing.
However, what we can say with certainty is that the weight hung upon that slender hook of dialogue is more than it was ever meant to bear. In particular, even if that episode was set in 2364, there's
nothing in it (or elsewhere in canon) to support the widespread assumptions that it was the very end of 2364, and that TNG S1 started at the beginning of that calendar year, and in fact that each TV season of 1000 stardate units corresponded to exactly one Gregorian calendar year, Jan-Dec. I've never understood how those particular assumptions caught on in the first place, since there's an awful lot in canon that flatly contradicts them.