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By order of the President, the flag shall be flown at half-staff upon the death of principal figures of the United States Government and the Governor of a State, territory, or possession, as a mark of respect to their memory. In the event of the death of other officials or foreign dignitaries, the flag is to be displayed at half-staff according to Presidential instructions or orders, or in accordance with recognized customs or practices not inconsistent with law. -- United States Code §175 Position and manner of display, Flag of the United States

So no, the flag shouldn't be lowered 'when the President decides they should be lowered'. This is a horrible act of evil but the lowering of the national standard is generally reserved for the deaths of principal figures rather than to score cheap political points at 0bama is trying to do. Some states lower their flags for combat deaths -- this is understandable and in my mind also appropriate.

You should also educate yourself on the difference between half-staff and half-mast. Flags over land fly at half-staff. Flags over water fly ay half-mast. The terms are not interchangeable.