Another Thought/Question on Benedict and Islam

There's a very sad and ridiculous irony, of course, in some Muslims violently protesting the Pope allegedly calling their religion violent.  The reference to the Byzantine emperor's statement about Muhammad so short and off-hand that Benedict obviously was not claiming the point to be true.  On the other hand, he did quote at much greater length, and from a more recent academic source, the idea that in Islam's view the deity is not by his nature ordered by reason and can act arbitrarily.  This is an important theological question, and I wonder if the assertion may not entirely true (even if it captures some general pattern in the Islamic view of the deity).  I know nothing about the issue, but I do wonder whether the history of Islam's posture on this may be a little more complex -- given, for example, the highly rationalistic and philosophical variety of Islam that flourished in the high Middle Ages (and that influenced both Catholic and Jewish thought).  Of course, this theological question is far different from the "stir up the streets" sound-bite about Muhammad that people are exploiting.  But can any co-blogger or reader tell us more about the theological issue?

Tom