You are correct. Ports are just a safe place to build ships, they're not involved with troop transport.
Are you sure about this? As I recall, ports are adjacent to both the sea/bay and land units. The "bridge" of ships must all be adjacent to one another in order to allow for troop movement.
If what you are saying is true, why then does Greyjoy start with ships in the bay and in the port?
Mind you, I only have the 2nd edition, so perhaps the question is geared to 1st edition, in which case, disregard anything I've said