The published text of the PM's speech makes it clear its based on the analysis (what you are calling "statistical probability") not debris or black box.
I don't know why anyone would find that disturbing.
Even if he had debris, for any given family there would still be some "statistical probability" that their loved one survived (infinitely close to zero) involving some sort of miracle, a hidden parachute or a missed connection, etc. Just as we'd discard such false hope, pretending that there is some other place folks ought to be looking or that there is any realistic chance that their family members are safe as hostages in some terrorist base.
It is exceedingly unfortunate that the data analysis was relatively slow (and the data itself was never open sourced); the delay resulted in much lost time and resources by many naval and air groups, and lots of needless gnashing of international teeth.
If there's any lesson here, the satellite data feed(s) should become a bit more formalized, and their release in the event of an accident be as standardized as the black box information. As for the $10/flight for the data, even if the airline doesn't pay for it up front, the data collectors should collect it, and save it until after the flight has landed. If it doesn't land, the airline can pay some much larger fee to get the data ahead of it going public ;>