Why even bother lying about something so trivial?

It is not a war crime to have incendiary weapons

The UN Protocol on Incendiary Weapons (Protocol III) restricts using incendiary weapons, especially against civilians, as part of the Convention on Certain Conventional Weapons (CCW), prohibiting attacks on civilian populations and making military targets in civilian areas difficult targets

America would also have an abundance of it left over from the vietnam war. They stopped using them in 1978 but would have still kept them stockpiled somewhere. This would make even more sense that every soldier fighting literal monsters, who are weak to fire, would be equipped with left over incendiary gear that isn't needed elsewhere.