I guess I was playing this wrong. I assumed that each player could choose one of the movement actions and perform that action (without spending any actions, hence "free"), including being forced to pay a card for "Move by Ship."
This makes me wonder if I've been playing something else wrong: I assumed that Railwayman and Sailor could use their special abilities during Government Mobilization to carry a passenger as well. For example, say one player is at Zaragoza, and the sailor is at Barcelona, a port city. Somebody plays Government Mobilization. I assumed we could use this to move the first player from Zaragoza to Barcelona, then move the sailor AND the first player to another port city (for free, using the sailor's other special ability).
I suppose you'll say this is also wrong?
Yes this is wrong. Unless the card specifically says a player performs an action, the cards basically function as a third party coming in and helping your team. For example, with a card that lets you remove disease cubes, you would not assume that you get to remove extra ones from a city with the rural doctor.