In law, and in Islam, forgiveness follows restitution. Apologizing admits responsibility. That admission makes settlement more expensive. Not only are people going to "pay" for this accident, but also people will "pay" more because of the apology.
Naveed Qamar, the head of Jamaat-ud-Dawah in Karachi, Pakistan said, “We don’t accept Obama’s apology. The Muslims don’t accept his apology, as it is nothing but a farce.” Without restitution, it is a farce; and the more sincere the apology, the greater the price of restitution.
In America's Judeo-Christian system, refusing a sincere apology is poor form, and so is meeting injustice with random violence. However, in Sharia systems, justice flows from balance. When salvation depends upon good deeds outweighing bad deeds (as in Islam), then justice depends on bad deeds and good deeds balancing between people too. People in Sharia systems restore balance by making and taking restitution, not by making and taking penance. In this case, random violence balances the offense and helps restore justice.
The Muslim and Judeo-Christian "dwellings" have different "house rules" for reconciliation. Americans cannot import Judeo-Christian "house rules" into Muslim "dwellings."
Patterns for reconciliation among Muslims do not involve taking responsibility and then apologizing. Rather those patterns involve blaming either circumstances or God ("It was God's will") and then asking for forgiveness.
In this particular situation, I understand that the Qur'ans were put in the trash because detainees had "desecrated" them by writing messages to each other in them. I would advise the President and his generals to say, "This is not our fault. Some detainees were desecrating Qur'ans by writing messages in them, and it is God's will that they have now been exposed in this way. Please forgive us."