The Inmarsat guy has six hourly ping times to work with. It should be clear whether the aircraft was heading towards his satellite or away from it over that time to an accuracy of somewhere in the region of 100 km per hour.
It could be confounded by a delay in the transponder reply, but there's no other factors that can affect it. Inmarsat must know a great deal about transponder delays, and they could run the same test on every flight since MH370 to see how wrong they are against actual flight tracks.
He has no information apart from the round-trip time to the aircraft, and his satellite over the Indian Ocean sees the whole Earth disk.
It is possible that some other mysterious geostationary satellite might have collected the signals too, which would help a lot in locating them, but I doubt the Inmarsat guy would talk about that on the TV.
If he had six hourly GPS positions reported in the replies, this uncertainty would all be gone. For a few cents per seat per trip, this would seem to be a good idea in future. Then again, the wreck of AF447 still took 2 years to find, despite much more comprehensive satellite signaling.