Mike, it truly does make a difference. I believe it is chased back to how the mortices are laid out in square rule, in part and more specific to the brace stock itself. The snapped line you see on Jim's brace is the referencing point on the brace stock not the edge of the timber, therefore you can not use it to measure on. In the case Jim presented that is the reason for the line. It is skinning a cat in a different way. today I laid out two long roof braces, running from the foot of one principal rafter to the top of the next, funky braces, the ends are swapped, anyway, I laid it out from the edge as you suggest. It is not my typical method, I use the same method Jim shows.
Open your view points up and see both worlds. Perhaps Jim can comment on that as well?
The "ideal timber size" is the snapped line and it meets the ideal timber within the post at the housing on the post, as proof.
The snapped line could be 1/2" , 3/4 or 1" or for that matter 0" in from the edge of the timber, it does not matter as long as the brace length is measured along the line. You will see some over hang if it is larger than 3/8" due to the housings/reductions being 1/2" deep.
This snapped line method also allows for layout of naturally curved brace stock. or brace stock that has dried and is not straight. Blessed you must be Mike, for having straight brace stock.