I am sure that neither of us believe that a Muslim who saws a Jewish American's head off (for being a Jew and being an American, in that order) chanting “Allah Akbar” is a “good Muslim”.
The relevant question is... Does the Muslim believe that by sawing a Jewish Americans head off while chanting “Allah Akbar” he is being a “good Muslim”. And the answer is YES. He does think it his religious duty to saw the heads off Jewish Americans while chanting “Allah Akbar”, and this is a COMMON current within Islamic thought, witness the words of one of the most famous and influential Islamic cleric of our age.
“To kill the Americans and their allies — civilians and military — is an individual duty for every Muslim who can do it in any country in which it is possible to do it, in order to liberate the al-Aqsa Mosque [Jerusalem] and the holy mosque [Mecca] from their grip, and in order for their armies to move out of all the lands of Islam, defeated and unable to threaten any Muslim.”
Osama bin Laden
Marxist-Leninist Liberation Theologians invoke the name of the Christian God to justify bloody Communist revolution and the destruction of the USA. Does the notion that Liberation Theology is not Christian also fall under the “no true Scutsman” falacy?