Here's a brief addendum inspired by a trip to Wikipedia (Inmarsat antenna locations) and PJ2's drawings.
Apparently the satellite likely in use is at about 15.5 degrees West. That means the antenna aim was on the order of 15 degrees off vertical. That means with its beamwidth if the antenna was aimed 15 degrees off vertical the opposite direction the satellite would still be well within the lobe perhaps at its 1dB or 1.5dB points ( 80% to 62% power points). Any transmissions would have been noticed.
(Visits to the Inmarsat site dug up pictures that were rather vague and no actual parking slot location. So I had thought the antenna was closer to 0 degrees via a really conservative guess.)