I think its more because Islamic forces (principally led by Turks at this point) had flooded into "Christendom" more or less identified with the ERE.
There was a strong "reconquista" mentality for Basilaioi, whether Makedonian, Komnenoi or other, both as guardians of the Holy places and as heirs of Rome.
The appeal of the Basileus Alexius to aiud against the tide of Islam sparked the crusades, hence I'd argue its fair to make the connection.