I dunno... I would think that our respective Churches think the other one has broken off and that theirs is the Church left to settle debates and teach Truth... for instance, on the divorce issue in the Eastern Churches, there must have been some kind of council convened to discern the teaching of the Church since the teaching changed a bit along the way?
I don't think there has been. The origin for Orthodox practice is in the Code of Justinitian and the Council of Quinisext if I am remembering my history right.
And I'll say again that the Eastern Churches approach to divorce is virtually the same as the Roman Catholic annulment. There was no change to accomodate.
Perhaps you are of the mistaken belief that the Orthodox Church automatically endorses every civil divorce granted? That simply is not true.