Starfleet and the Melkotians set Kirk up
The opening of the episode seems quite out of character for Starfleet, as their order blatantly violates their own Prime Directive. Enterprise was sent to make contact with the Melkotians "at all costs," to the point that Kirk couldn't even turn back when the Melkotians explicitly warned them away. Subsequently, Kirk and company are run through a scenario that turns out to be a Secret Test of Character. What really happened is that the Melkotians had already secretly made contact with the Federation, but expressed reservations and wanted them to prove their good intentions. Thus they arranged this test. Starfleet sent Kirk in knowing he could pass, but kept him in the dark about the full nature of the mission.- The state of the Melkotian civilization would be such that the Prime Directive would not apply to this situation.
The Melkotians chose which bridge personnel went to the planet
The Main Characters Do Everything on the main page is justified because the telepathic aliens running the show would have wanted the ones responsible for trespassing in the first place, and could be influencing Kirk's mind at the time. Including Scotty in a landing party is almost never done unless the problem involved is mechanical in nature, as he is the third in the command chain (and the First Officer also happens to be the Chief Science Officer whose presence is necessary for most landing parties). It's probable that the Melkotians grabbed all the important department chiefs as well as the Navigator who brought them there.