Robert Comsol wrote:
If I remember correctly, the Talosians lured Pike and his Enterprise to their planet with a fake (mind produced) distress call, this already established their capability to have telepathic influence over great distances.
Like the episode establishes, there's no way to tell whether a given thing is illusion or reality. Quite possibly, the distress call was a perfectly physical radio wave, just like our heroes thought. No need for long range, then.
This is in line with Spock's capability to establish telepathic mind links over great distances (e.g. V'ger's call in TMP).
Good point, and already sufficient to explain all of "The Menagerie".
As for details such as how just Kirk came aboard in a supposed beam-for-two event, let's remember just how
the Talosian mind control works. It's not a case of them directing their pulsating foreheads at specific people. Rather, the entire area, the entire landing party, the entire starship starts to see things that aren't there (the survivors), not to see things that are there (the elevator), to do things they don't even realize they are doing, despite having already reasoned that they must
be doing it themselves (going through the memory banks of the ship)... AND THE AUDIENCE IS AMONG THE VICTIMS!
That is, we don't see Spock pressing buttons to send Talosians information from the ship's databanks. Instead, we see the illusion of him staring helplessly as the databanks send this information "all by themselves".
There's no need for details, as the Talosians project entire story arcs that their victims find utterly plausible from start to finish. If something doesn't add up, the victims fix things so that everything makes sense again. And again, this applies to the audience as well. We're supposed to see a happy end, but what we see is probably 100% false. We have no real reason to assume that there ever was a Vina, or that Mendez was an illusion, or that the real Mendez sent any messages, or that Pike is happy down on the planet. It's just a satisfactory wrap-up that allows the heroes and the audience to leave the adventure behind.