You didn't. But if the burning provokes more violence in theater, then the burning becomes a killer of our troops. Tactics must change to suit the situation, particularly when you, at home and in a confortable place, can affect the well-being of those who defend your Freedoms. Why use your Freedoms to endanger your benefactors?
If backing down gives the enemy a new victory to proclaim over American weakness and increase their recruiting, you're fine by that? The politics of appeasement serves their interests, not ours.
Have you considered that by reacting positively to the enemie’s emotional outburst you are empowering them and, by extension, putting our troops at higher risk?