I've wondered about that too. Obama after all was supposedly a constitutional law professor and voted for the senate bill declaring McCain to be natural born.
My guess is that Obama KNEW full well he failed to meet the NBC requirements. He probably figured he could rely on the race card and implicit threats of riots and civil unrest if his eligibility were ever questioned. The fact that the major media were solidly running interference for him probably didn't hurt. You can see how they're still doing it, ridiculing legitimate questioners as nutcase "birthers."
What makes you think he didn’t use those tactics you mentioned? After all, he went over to Kenya, campaigned for his cousin, AGAINST THE LAW BTW, and showed him how it is done.