That is not a bad response from his position. From say a game theoretic point of view.
Imagine is he is not the president but say a mafia boss, maybe a powerful drug lord. And it turns out one of the drug mules for a competing drug gangs gets murdered by Obama's men. Now, war is about to start. And all the drug lords have a meeting. Obama can claim he didn't personally order the murder and he didn't know it was about to happen. He has men working for him who receive general instruction like "keep the product flowing no matter what cost" with specifically no concrete instruction (especially in written form). Now that protects him. If worse comes to worse, he can simply replace a scapegoat low level employee and keep the organization going forward. The same modus operandi is probably at play with regard to a lot of this stuff from the White House.
On the other hand, the POTUS is at least supposed to look powerful in the eyes of the citizens. By recognizing that he doesn't know (and can't know) what's going on, he is announcing to the world that he is a puppet and that the POTUS is nothing but a servant to higher interests.
Imagine is he is not the president but say a mafia boss, maybe a powerful drug lord. And it turns out one of the drug mules for a competing drug gangs gets murdered by Obama's men. Now, war is about to start. And all the drug lords have a meeting. Obama can claim he didn't personally order the murder and he didn't know it was about to happen. He has men working for him who receive general instruction like "keep the product flowing no matter what cost" with specifically no concrete instruction (especially in written form). Now that protects him. If worse comes to worse, he can simply replace a scapegoat low level employee and keep the organization going forward. The same modus operandi is probably at play with regard to a lot of this stuff from the White House.