Hi S,
I believe square rule was developed using snap lines BEFORE layout from an edge became prevalent. This was because the earliest proponents of square rule were using hewn timbers and then sawmills became common later (at least for bigger timbers). See Jack Sobon's monograph "Square Rule vs. Scribe Rule", available from the Guild (I think). I personally don't see much practical difference in laying out from a centerline or an offset line, and would be curious to know how the methodology would differ in your technique. It's wonderful we can always learn something new in this craft.
If you look at James Mitchell's book 'A Master's Guide to Timber Framing" he uses a method he calls "Virtual Rule", which (in my opinion, and this could open a can of worms) is a just a variation of centerline square rule. The use of housings and thus framing to a perfect timber within is what distinguishes square rule in my view, whether laid out from an edge or a line.
I'll check out the link you sent for clarification and could be convinced otherwise. Thanks.