The government is not above the law; they interpret it similarly to other gun owners. Even in states where open carry is illegal, you can carry however you choose in your own home or place of business, and may grant permission for your family or employees to do the same. You see it everywhere in gun stores; every employee of that store has a hip holster with a 1911 cocked and locked in it.
The government does the same thing; officials of the state are allowed to carry in their place of business (the government building in which they work) IF their boss allows it. Said boss, like any private employer, largely has the right to deny carry on his property. Officers of the law, including uniformed officers in court, must carry as a part of their job description, and are therefore allowed to do so in the government buildings they spend a lot of time.
The President, like any other citizen, is allowed to own firearms and to keep them in his place of residence. He may however be subject to rules regarding WHERE in the House he is allowed to keep them (probably a secure, guarded locker in the basement along with SS armaments), as though it may be his residence, he does not own it and he has far more visitors of varying familiarity than you or I. I'll bet you anything that any guns the President owns, kept safe along with the President by two Secret Service tactical teams and a plainclothes SS team, are far more secure and far less likely to be used illegally than your own. And think of this. If the President of the United States, the leader of the free world, does not have the RKBA, what the hell chance do you have?