[Torie]

the Byzantines were not in control of the lands where the Crusaders originated was because of the earlier Arab conquest of the southeastern provinces.

???

[AntiGuv]

When Heraclius was emperor at the time of the Muslim conquest the Byzantines still ruled Italy and the south of Spain. My supposition is that had the Byzantines held against the initial Arab attack they would've extended their rule across Western Europe (in particular Gaul) long before the Crusades. It was due to the post-Arab decline that Italy was lost by the Byzantines (and of course the Muslims conquered Spain).