Ok, so if you follow all of the cross-references in the various parts of ISO 128 regarding cross sections, you eventually get directed to ISO 128-40. The exact statement regarding the 'cutting line' (the term used by the standard) is:
"The position of the cutting plane(s) shall be indicated by means of a long-dashed dotted wide line (cutting line) of the type 04.2 according to ISO 128-24:1999 or 04.2.1 according to ISO 128-23:1999. A straight cutting plane shall be drawn to a suitable length for legibility (see Figure 1).
If the cutting plane changes its direction, the cutting line should only be drawn at the ends of the cutting plane, where the cutting plane changes direction (see Figure 2).
The cutting line may be drawn to its full length (with a long-dashed dotted narrow line of the type 04.1 according to ISO 128-24:1999 or 04.1 according to ISO 128-23:1999) if necessary for its legibility."
So it seems that if Fusion 360 is going to be fully ISO 128 compliant, users need the ability to toggle on/off or trim the cutting line as we see fit.