It turned out that after the previous (Air France?) loss of aircraft, Inmarsat's operations team/executive decided that they should preserve data about the Burst Timing Offset (BTO) and Burst Frequency Offset (BFO) of every transmission to/from aircraft instead of discarding it as unneeded data (their disks were filling up). That data records the returned ping frequency and timing offset (hence the names) of the plane's transmissions to/from the satellites, even if it's just for a handshake, and no meaningful voice/data content is exchanged.
After all, if a perfunctory handshake message contains no content, why save something as esoteric as the Doppler-shifted frequency you received it back on, or the timing difference?
The executive in charge of that said, impressively, "we didn't exactly know why we might need it in the future, but we thought we should save that data." (paraphrasing, can't quite find the original quote right now)
That frequency + timing offset was the key information in figuring out what radial + distance the plane may have been flying on, for 7 hours after all other systems stopped reporting, based on the hourly handshakes/pings of the sat-phone system. All other data reporting systems had gone offline or out of distance. They tested it against other aircraft (in same geographic area, time, and of same type even!) whose positions were known, and had confidence it was trustworthy enough to base the search areas on.
It was a fascinating read to me at least.
https://www.cambridge.org/core/journals/journal-of-navigatio...
and more generally:
https://en.wikipedia.org/wiki/Malaysia_Airlines_Flight_370_s...