Most of them probably don't care all that much. As people have noted, they destroy Qurans all the time when they attack "heretical" Muslims.
Even if they did care about being 'religiously correct', it still causes no problems anyway:
"One who previously engaged in jihad knows that it is naught but violence, crudeness, terrorism, frightening (others), and massacring—I am talking about jihad and fighting, not about Islam and one should not confuse them... Thus, the Companions (may God be pleased with them) understood the matter of violence and they were the best of those who understood this after the prophets. Even the Friend (Abu Bakr) and Ali b. Abi Talib (may God be pleased with them) burned (people) with fire, even though it is odious, because they knew the effect of rough violence in times of need...We are now in circumstances resembling the circumstances after the death of the Messenger (peace and blessings be upon him) and the outbreak of apostasy or the like of that which the believers faced in the beginning of the jihad. Thus, we need to massacre (others) and (to take) actions like those that were undertaken against the Banu Qurayza and their like. But if God should give us power and we take control and justice spreads, how tender the people of faith will be at that time and they will say to the people: "Go, for you are free." [from the jihadi text] The management of savagery
Basically their 'scholars' have created rulings that basically say 'anything is permissible' as they are fighting for the very survival of their religion, so it is acceptable to transgress the laws of the Sharia if it helps defeat the infidels. Sort of a 'lesser of 2 evils' logic.