I think that one of the cruxes of the matter are where the layout ends and the joinery begins. In my case, I LIKE fully housed joinery. I like it structurally and also for the flexibility it gives me in planing. It is not a decision that was necessarily made in response to my layout method. In fact, I went to fully housed joinery before I ever used center line layout. I don't see that it would be hard to use center line layout without fully housed joinery as well it would just have to incorporate some aspects of stock preparation.
My adaptation of the layout method that I learned from Jay, is probably not in accordance with traditional Japanese practice, nor is my suite of joinery. My combination of layout, joinery, and structural preferences are in the end my own custom combination created to suit my priorities and tooling preferences. One could say that I took an Eastern layout method and married it to a more Western joinery.
When you get right down to it, when most people talk about square rule, they are talking about reference face layout. Any mention of snap line square rule gets treated as a subset of the methodology, particularly useful on hewed timbers. It still seems to follow most of the other attributes of square rule such as offset tenons.
Another compelling reason to count center line rule as a separate method is that it is the dominant layout system for entire cultures with a unique tradition and heritage. So, even though center line rule and snap line square rule have similarities, they have no common root. I can't argue the historic particulars as I have no first hand in depth knowledge. Perhaps Jay will have something to say in that regard. The forum thread that I referenced in my earlier post did seem to draw a hard distinction between center line rule and snap line square rule however.
I do realize that I should be more careful with my own terminology. Sometimes I just say snap line rule, where I should more properly say center line rule. It turns out that words matter!