Very much agreed. Once you acknowledge satire and parody as two different entities, then you can start separating series that fall into either category.
For example, Panty and Stocking is a satire (deconstruction/subversion) of Mahou Shoujo. It also had a few individual episodes that were parodies of Transformers, Saving Private Ryan, and zombie movies, but that didn't mean the whole thing was a parody. The whole is a satire with parodies peppered in.