Only Allah?

If the statement that Allah is the only God is a fact, then even idol worshippers worship only Allah for the simple reason that there is no other God to worship. Then why do Muslims say that idol-worshippers are worshiping other Gods? Because Islam has not been able to prove that Allah is the only God. Islam is just a belief. While one fact cannot be as good as another, because a thing is either a fact or not - one belief can be as good as another because incontrovertible facts need not be involved therein.