In a fascinating but brief column, Dr. Tawfik Hamid of the Potomac Institute for Policy Studies suggests the US military should use the Quran to influence the Islamic population’s reaction to their conduct [emphasis added]:

The Koranic text can actually be used in such situations to control the Afghan anger and prevent its spread. In fact, the religiosity of people in these parts of the world makes the use of religious text more effective in controlling people’s anger than using formal apologetic approaches.

(Dr. Hamid joins a chorus of other resources who have written on the issues of “apologies” in the Iraqi and Afghan cultures.  They are not viewed the same way a Western citizen would view an apology.)

Dr. Hamid suggests several Quranic texts that might be used to “defend” the US military from the anger of local Afghan Muslims:

The Koran states clearly that the Lord forgives unintentional mistakes and only considers an action as a sin if it was intentional — Koran Al-Ahzab 33:5, “But there is no blame on you if ye make a mistake therein: [what counts is] the intention of your hearts: and Allah is Oft-Returning, Most Merciful.”

[Afghans] must bring evidence that the intention of the NATO personnel was to insult the Koran — as the Koran itself describes those who accuse others without having evidence as “dishonest” people (Koran Al-Naml 27:64 “Or, Say, ‘Bring forth your evidence [proof], if ye are telling the truth!’”).

The Koran forbids any angry reaction against the NATO soldiers who actually did not commit the burning and are likely to be against it.
 
The Koran states clearly in four different positions that no one should be punished for the mistake of another person [Koran: Al-Isra 17:15; Al-An’am 6:164; Fatir 35:18; Az-Zumar 39:7 [“Nor can a bearer of burdens bear another’s burdens.”]

In point of fact, the US military has previously described its efforts to

turn Islam into a weapon against the Taliban.

Via the Journal of Faith and War.