The root of the problem is that "Balance of Terror" categorically declares that invisibility of any
sort is astounding, theoretical and all-new to our heroes.
Spock has some ideas about the technologies needed to accomplish this, perhaps correct, perhaps wholly erroneous. But he has never seen an invisible ship, so to speak, and has never heard or read of anybody who would have.
This is anomalous even in the context of TOS itself, where invisibility subsequently is rather humdrum. Heck, the Thasians in "Charlie X" had something Uhura considered a "ship", and that one appeared out of nowhere, too!