You are correct that for a stationary use, Inmarsat antennas can be manually pointed. On a moving Vehicle, it is usually necessary to have an antenna that can track the satellite to maintain an Inmarsat connection.
Are you sure that the car antenna you mentioned was not for an Iridium? Irdium phones, even when used for data, do not need to be pointed.
My bet is that the Inmarsat antenna on this plane has its own GPS, and that GPS is the source of the locations in the "pings".