Re: '300 years ago' , in this film's context, was the 1950s!
Remember also that when Kirk said to Khan that he'd been sleeping 200 years in "Space Seed", the Trek timeline hasn't been set in stone. "The Squire of Gothos" suggests that TOS is set around 700 years into the future.
Star Trek Imponderables
, fun mashups of Trek's biggest continuity errors! Ep1