Did a Byzantine emperor really start a war on icons, and how would we know?

Yes, there were two periods of official opposition to icons, but the familiar story of how the first began is shakier than it looks. The First Iconoclasm occurred between about 726 and 787, and the Second between 814 and 842. By the traditional view, it was started by a ban on religious images by Emperor Leo III the Isaurian, continued under his successors.

The classic account says that Leo ordered an image of Christ, prominently placed over the Chalke Gate of the Great Palace in Constantinople, replaced with a cross. But accounts of the event were written significantly later. Patriarch Germanos' letters from the 720s and 730s refer to Leo III, often presented as the original iconoclast, as a friend of images. Today this interpretation is in doubt, and the struggle may have begun in the provinces rather than the imperial court. Leo's actual views remain obscure.

The reason lies in the sources. Most surviving sources were written by the ultimate victors, the iconodules, who defended images. Most iconoclast texts are missing, including a proper record of the 754 council, and no account of the period written by an iconoclast has been preserved. Many texts were undoubtedly "improved", fabricated or backdated by partisans.

So the honest answer is that a controversy over images did happen, and that its first act, as told, rests on evidence written by the other side.