«هذا الشيء إما شجر أو حجر»
This thing is either a tree or a stone.
One and the same thing cannot be both a tree and a stone in the same relevant respect. Therefore the two alternatives cannot both be true.
Yet the thing might be neither a tree nor a stone—for example, it could be a bird. Both component claims would then be false without violating the rule of māniʿat al-jamʿ. This form excludes joint truth, not joint falsehood.