@Frequent Traveller
I was envisaging they would have their own antennae with the phone, or could rig one up. But your point about them giving themselves away is exactly what I was getting at.
Like I said, we don't know exactly what data Immarsat relayed.
I'm just postulating that the data may well have included satphone calls.
They wouldn't actually give away their location. As has been noted, you can't triangulate off one or two satellites.
@ Mixture
I take your point about using the satphone handset in a car. In the plane, perhaps even with an antennae across the cockpit windows, they may have more success.
I'm happy to be corrected. The people who planned this excursion are rather clued up.