Correct. Fletcher starts by surveying Byzantine writings on the Arabs before Islam even existed, which differe little from later writings about muslims. Then he argues that the principal attitudes between Islam and Christianity were indifference (by Muslims towards Christians) and ignorance (by Christians towards Muslims). He also claims that at the time on the Islamic expansion, Islam only could only fit within Christian worldview as a heresy (and Mohammed as a false prophet).

I don't think the East/West split or even the Schism play a role in Fletcher's narrative. Can you expand on that?

Also, while Byzantium (and Spain) were border regions with Islam (and Fletcher spends a lot of effort studying the frontier dynamics), Western Europe (organised around the Pope and the Emperor) had little contact with Islam. In addition, the Crusades were a Western phenomenon having to do with religious-secular power conflicts, and Byzantium suffered a lot of collateral damage.

Those whom the Gods wish to destroy They first make mad. — Euripides