I see your point, Carjockey, and we sort of agree. The points you make weren't what the story was going on about.
If the initial reaction was to begin with own assets, and they then later called for help because their first estimate on where to look didn't pay off, how is that different from usual procedures?
The larger question strikes me as
"What was going on between about 2 in the morning and 8 in the morning as it became clear that the aircraft wasn't going where it was supposed to be going, and had been out of contact"
rather than
"you went looking for it and told nobody else that you went looking for it."
If the ATC's, military and civil aviation authorities of neighboring countries had been informed of the situation immediately, the chances of 370's flight path being tracked would have increased dramatically and we would not be faced with the present situation.
Not sure if that is true or not, but my gut feeling is that you are right.
Cheers.