Inmarsat have many hundreds of thousands of flight records that they can test their method against. I'm sure they wouldn't broadcast faulty information.
I believe their data. It's the fact that they are not accident investigators that concerns me. Any good accident investigator knows to be wary of projecting their own bias onto the data instead of letting the data takes it where it leads them. In fact, the fact that the normal assumption is that delay=distance makes me even more wary of it.
Several people have suggested that the plane flew low over the water in order to avoid radar detection. Flying low over the water could cause what is known as "tidal fading" which is interference as a result of multipath reflection off the surface of the water. It's theoretically imaginable that this tidal fading could cause the distance calculations to be messed up in unpredictable ways.
So I'm not wary of their data, I'm wary of their assumptions they are making in analyzing the data.