/u/Naharion

From where did you hear this? It's nonsense. Neither the HRE nor the Catholic Church was a monolithic centralized entity. How can one fragmented body rule another fragmented body? Their respective degrees of fragmentation were correlated but not synchronized. The span of the HRE never came close to encompassing all of Europe.

Good books on the HRE provide plenty of counter-examples and counter-arguments against that claim, for example see Wilson's The Heart of Europe, which starts off with a great exposition of how complex the relationship between the (what was to become) HRE and the Catholic Church.