Will I should clarify,
Material prep is not here the result of half scribe, but rather vice versa. The half scribe system arises as a result of the high level of preparation that goes into the material because of the styling of the architecture.
The carpenters are not putting extra work into the frame to tediously prep the material so that it can be laid out with a half scribe system. They are tediously prepping the material because that's just their way. Because the architecture calls for extreme precision all around.
Tehn, since the material is extremely accurate, they need only use half scribe.
As to bow and twist,
first of all material selection is extremely picky. Second of all, timbers are small in cross section and shorter in length. This helps to minimize these concerns. But just to be sure, mortise faces are always cut square to the reference if they deviate.
Now keep in mind, I was taught that 1/16" is a large gap in a joint, the tolerance you cut to in a hidden joint.
AS to the development of square rule, I don't think we'll ever really know. It is likely, a lot of people came up with ideas along those lines over the centuries. The genius isn't often the one who comes up with something revolutionary and unprecedented, but one who puts old ideas together in a new way. I'd bet you a nickel that happened here. We're likely to find hints of square rule all over Europe. We don't know the half of the story, and so many little details get passed over. Swiss carpenters and architectural historians, for example, don't ever talk about layout because they don't think about it. It's just how it's done, that's all. There's likely to be a lot of little gems like this throughout Europe.
But if we really want to look for deeper influences, let's skip out from timber framing for a little bit and look at log building. Here we find something that applies the concepts of square rule, but for a different purpose completely. We have joints designed with normalized and reduced connections with timber reduced to a common dimension at these locations, but not to simplify layout -no these buildings even today are fully scribed- the technique here is used for the purpose of creating joints that retain their integrity as the walls move and settle, or as a means of connecting a number of horizontal logs or timbers into a single upright. Log ends fitted into a groove in a single upright need to be reduced to a common thickness.
But nonetheless if you didn't know about the problems of settling, movement, etc. and you looked at these joints, they would strike you as remarkably square-rule like. Food for thought.