That's true, and that might account for a day, perhaps two, before discovering the military radar data. But they didn't start searching west until four days after the disappearance, and didn't stop searching east until even later. Even crazier, they started searching west while denying reports about the military radar data. That military radar information leaked to the public three days after the plane disappeared but was denied until a couple of days later. Crazier still, Wikipedia says:

> According to the Vietnamese Deputy Minister of Transport, Pham Quy Tieu, "We informed Malaysia on the day we lost contact with the flight that we noticed the flight turned back west but Malaysia did not respond."

Malaysia had all the info they needed to know that the plane had not crashed into the Gulf of Thailand almost immediately. Ideally they would have acted on it right away. Realistically, I can understand a day or two of delay as they look into the obvious things first and try to confirm the other data. But to wait so long and ignore so much is well beyond what ought to have happened.

Edit: especially in the 9/11-paranoid US and other similarly fearful countries, the plane would have been noticed on military radar in real time and would have been intercepted right away, and this whole question of who knew what when and how long it's reasonable to search in the wrong place would have been avoided because the fighter pilots would have watched the thing sail off with their own eyes.