The first time "Kirk"/Garth fumbled the countersign thing, Scotty realized there were enemies down there on the station, people he couldn't trust either with their facts or their actions. But Scotty had no real idea what was going on down there, and whether the team he decided to try and send down there should release, arrest, stun or kill this possibly-not-Kirk.
Now Kirk or "Kirk" is again fumbling the codephrases,
and asking for security to beam down. So, should Scotty beam down security when that is the very thing this suspicious possibly-not-Kirk
wants? It's quite understandable that Scotty does
not do that right away.
It's highly probable that the use of a code phrase is not standard Starfleet practice, or else Garth would be aware of it and Scotty wouldn't comment on it as if it were something Kirk came up with specifically for this occasion.
Let's remember, though, that Spock says the
Enterprise has visited Elba II at least once previously, before Garth was there, and Kirk is first-name friends with Governor Cory; it's possible in theory that the
Enterprise is the
only vessel that ever visits the facility, and Kirk (a veteran of "Dagger of the Mind") has come up with the security protocols of the facility and its interactions with its one and only supply starship. Elba II probably isn't an old facility, after all: it exists as the terminal stage of a modern criminal treatment system only recently established by Dr. Adams.
Could Garth pass a medical exam?
Does he shapeshift or does he project illusions? The Salt Vampire
would have passed a medical, as it always showed what people wanted to see, regardless of what it really was. A Founder would have passed because it was a perfect shapeshifter. A Chameloid might have passed because it was a true shapeshifter (when it looked like a little girl, it was also physically sized like one, and could slip out of its chains), but was it a perfect one?
Garth is shown mutating his clothes, not just his body. This means he either goes around naked, or projects illusions. Would the former come naturally for somebody who only very recently was a human(oid) being?
"Whom Gods Destroy" is fun for being so ambiguous, yet not contradictory. There are good concepts there, and if one dislikes any one of them, one can always decide it's one of Garth's delusions.
Was Kirk once a mighty warrior? Perhaps he admits to that only to placate the madman. Does Garth have a powerful explosive? Possibly he only has an ordinary one, but thinks that his rather unconvincing demonstration will nevertheless cow his enemies. Is Marta really Orion? Who knows? Etc.
Timo Saloniemi