Was the problem Church teaching, or the way Church teaching was being presented? 

Given that Protestants challenged the institutional structures of the Church, it seems only natural that a consequence of this would be an an exaggeration of those same structures from the Catholic side.  

I am not sure Vatican II was a "reform" so much as it was a restatement of Catholic teaching in modern language. Instead of putting Church teaching in the typical "If anyone says X let them be anathama" Vatican II put Church teaching in a positive light.  

I would argue that the division in our Church comes not from "reluctant explanations of the reformers..." but over opposing interpretative systems.