Ding ding ding ding, we have a winner.
The very LAST thing we would want the world to know is that we know its in Pakistan. Its called OPSEC. We would want the bad guys to think we don't have a clue.
They are certainly watching the news and will certainly use this plane before we can do anything about it if they think we are on to them.
So...you are absolutely incorrect in your assumption about this being a White House thing. If they are behind the misdirect...then they are doing the right thing.
If you've been in the military, you will understand this. Its a classic counter-intel operation. Misdirection until you can move against the target. Best to sneak up on the rat and kill him when he thinks you are in the other room....rather than announce your coming for him.
The general is doing his country a disservice by announcing this. He needs to keep his mouth shut if this is true. That's all we need is for the cat to get out of the bag that we know its in Pakistan...and thus move the terrorists to their next target before we can get in there and kill them.
If he was back in the military and some news guy was ruining his OPSEC...he would be having a stroke.