The ships controlled by the AI can cross and even end their turn in the same tile as in which a player controlled ship is located. It does not matter whether there is peace or war between the two involved races.
What i did: i parked a scout on ship graveyard, because the Krynn had a survey ship near, and my survey ship was still far away. However the Krynn survey ship simply entered the same tile and obtained a lost survey ship.
The screenshots:
Bottom-left the ship info for my selected Terran Lost Scout Ship. Center-left Krynn survey ship is projected on top of my ship. Center-right the newly Krynn acquired "Lost Survey Ship" projected below a Elerium resource.
Bottom-left the ship info for the selected Krynn Survey Ship. Center-left and center-right are the same as in the previous screenshot.
