Correct and I agree with you. I only mention it because many try to use that as a reason or justification for the Crusades.
Pope Urban's reasoning revolved totally around expanding the influence of the western Church. Nobody in Constantinople asked for the crusades.
Not true. Alexis pleaded with the Pope and others for assistance leading up to the First Crusade.
Didn't turn out perfectly well for him or his successors, but the Byzantine Empire certainly had a good bit of pressure taken off it for quite a while.