My impression was that he could have stopped the assault at any time by returning the kidnapped soldiers and accepting a negotiated settlement. The fact that the soldiers have still not been returned belies his comments in this interview.
Hostilities would have halted by Israel, at least for awhile, if Nasty had just stopped the rocket attacks. I agree with your assessment. He could have stopped almost all of the destruction if he really didn't want it. He's a liar.