Well the President shouldn't know about these things. That's what his Secretaries of State are for.
The President is the Head of State. I put those capitals in for a reason. It is an almost religious position. A large part of the authority and legitimacy of the state is invested in the current head of state and their behaviour has to be of an appropriately high standard. This is difficult under an executive presidency like the US, but the principle still applies.
Of foremost concern here is the simple principle that there are certain things the president should not see or hear. Sometimes countries need to spy on others, or assassinate people, or steal, or whatever. But there is absolutely no reason why the President needs to be told about these things. The only time the President should hear about things like this is in the newspapers, shortly before he makes a pledge to hold the guilty responsible.
The President is not going to be able to uphold the law if all of the lawbreakers make him an accessory before or after the fact as a matter of routine.
This is to say nothing of the loss of legitimacy that comes with being involved this close to the coal-face of the uglier side of state operations. As bin Laden was being killed, the President should never have been allowed into a room where live images of people being shot and killed were displayed on screen. Without exaggeration: His aide-de-camp deserves to be court-martialed for allowing that. The damage to the image of the US President as a head of state will take decades to undo. Heads of State do not watch gunbattles on live feeds.
There is Politics, or PR-Politics as it is practised today. There is Government, and the business of running it. Then there is Diplomacy and grand and murkier business of deal with other countries.
And finally there is Statecraft, the art of running a country wisely. No PR-man, economist, scientist or other technocratic advisor can speak with any authority on this most essential of topics. It is nebulous, yet essential to all actions of the state. Systems ; political, economic, national, international, are made or unmade by the actions of senior officials and heads of state. It is essential that these actors have the gravity and respect necessary to inspire confidence in their actions. It is simply not possible to do this effectively if you have been repeatedly seen emerging from the latest political abattoir, covered from head to twitter feeds in fallout gore and scandal. Heads of State have to be above such things.