Chased back means chased back to the origin, the origin is square rule, the truth is found in that which lies beneath the surface of a timber. Snapped lines bring truth to the timber. In the brace example if one was using rough sawn stock or even planed stock it may have some bow in it, or other defect. If it is not straight the act of drawing 45 degree angles on the ends may result in angles +/- the desired result. So, gaining the end cuts on your brace stock is guaranteed when using a line.
