I think we need to believe our eyes instead of what someone says.
On this vein, let's rationalize...
SB 11 is located on a planet; some imagery makes it look like a habitable one. Might well be that SB 11 is but one installation on an inhabited world, rather than the entirety of human/UFP presence on that world.
So, while some people might prefer staying at the local drinking establishments, most would quickly depart the starbase after arriving if they possibly could. So let's say the skippers ultimately picked for Kirk's court-martial had already gone to the next city when Stone made his decision, after having had a meeting at the starbase and a quick pint or two, and had to be summoned back... That'd cover the "on their way" part nicely enough.
Why these three were selected, rather than any other three out of the no doubt dozens of skippers and several star ship skippers currently on the planet, isn't that much of a problem. Weird rules govern the selection of jury members everywhere, in civil courts and competitions of all sorts. Hey, for all we know the three were sharing a drink with a court clerk and a lawyer at the beginning of the story because they had just finished processing a previous case! Stone might have picked them for their expertise in the field.