Breaking down the Menagerie:

why is the Starbase rep looking up into the atmosphere?

as if she's going to see this beam fizzing through the air - is she like
looking for the direction from which they are going to be beaming?

wouldn't Spock have devised a more elaborate ruse to ge the Enterprise to
Starbase 7, something completely *unrelated* to Cmdr. Pike, so as not to
arouse suspicion?