I think we all agree (and hope) the authorities have more information than has been publicly released.
I wonder if the Inmarsat satellites are really the information the authorities are going on. It certainly does sound plausible. However it does seem an odd coincidence that the claimed level of precision should just happen to produce a result of 40 degrees.
It also took a few days for this information to come out. While this delay does make sense, it also makes sense if there was a need to develop a plausible explanation in order to protect true capabilities.
The US has likely invested heavily in the area of tracking airliners - especially post 9/11 when primary radar was unable to track large jets flying around 2 of the most important US cities. They also have plenty of experience tracking phones - and have spent many years delivering "air mail" on the basis of real time phone intercepts.
We will likely never know. But it is possible the search is not quite the needle in the haystack that it appears. Hope so anyway.