Maybe I don't yet understand the system, thus please bear with me. :)
From what I understand people willing to travel go to stations with passenger service, however I have a port that has only freight services, still, some passengers turned up and are waiting at this port for a ferry that will never arrive there. As usual, here's a screenshot: http://i.imgur.com/NYIotvp.jpg
Looks to me that a group of people walked from the passenger dock to the cargo dock, although only cargo ships depart there.
Does this stop have a foot connection to another stop which does have passenger service? (i.e. is it within the coverage radius of another stop?)
Yes, what Carl says is correct: this can happen with foot connexions.
Yes, there is a dock with passenger service only 7 or 8 tiles away, that's also the station where the group of passengers originated.
I fast-forwarded the game for half a month and the group of passengers is now back at the station where they came from, let's claim they just wanted to see the ships pulling in and out of the cargo dock. :)