Those popes were very specific about it being the Roman Catholic Church.
I would like to see some source that indicates that Pope Innocent had some other church in mind than the Roman Catholic church, of which he was the head.
What other churches were in existence in those days to which he might have been referring?
So specific that they never once used the term "Roman Catholic"?
I would like to see some source that indicates that Pope Innocent had some other church in mind than the Roman Catholic church [sic], of which he was the head.
He may have been, but that's NOT what he wrote, he said "Church of the FAITHFUL." You see, Church teaching on this is based upon what the Holy Father actually wrote, not what some people think he meant.
What other churches were in existence in those days to which he might have been referring?
Oh I don't know, maybe the Orthodox? For those who don't know, the Orthodox were the ones who realized that it was possible to break from the papacy WITHOUT embracing heresy.