... namely, that Vulcan medical facts are unknown to their close allies, the humans.
Except TOS never claim that Earth and Vulcan are particularly close, even if allies. Journey to Babel shows that the various members of the Federation are far from close to each other.
But it still looks really silly in "Amok Time", "Journey to Babel", "Operation: Annihilate!" and to a degree in "Dagger of the Mind".
Both Amok Time and Dagger of the Mind involved aspect of Vulcans that they found deeply personal. Enterprise revealed that in the 22nd century, the ability to mind meld was a dirty little secret, and a social taboo. A hundred years later, that might not have changed in Vulcan society.
And why would the ability to mind meld be considered "medical information" anyway?
Similar with the events of Amok Time, this was a closeted cultural aspect of the Vulcans that they wouldn't have wanted put into a public database. While Spock likely isn't the only Vulcan in Starfleet, his presence on a mostly Human ship might still have been a rarity. If serving aboard say the Intrepid, his "amok'ness" wouldn't have been a problem, and space fairing Vulcans probably have a quiet internal policy to deal with this when it arises.
In the case of Journey to Babel, McCoy had enough information on Vulcan anatomy to perform a purely medical procedure like a heart operation on Sarek, there was nothing cultural about that.
With Operation: Annihilate!, I figure what actually happen was that the "inner eyelid" muscle closed hysterically, and locked shut, effectively blinding Spock. In time these muscles naturally relaxed. This was a unusual event and wasn't in the purely medical database that McCoy did have available to him.
In all honesty, regardless of Spock's species/mixed species, McCoy should have seen the problem when he examined Spock's eyes.
