Is this "Sympathetic fight response" axis accurate?
The typical axis of the fight response is depicted in Fig. 1.


Fig. 1. HPA axis. Source: Social Psychology principles

This axis is the hypthalamus-pituitary-adrenal axis, or HPA axis. It mediates not only the fight response and is typically referred to as the fight-flight-fright response. It is the central stress response system that prepares the body in a fraction of a second for survival, basically under the influence of adrenalin and cortisol produced by the adrenal glands.  

The circuit you are describing, by the looks of it, is more typical for a reflex arc (Fig. 2.).


Fig. 2. Reflex arc. Source: Sweetibnotes

A typical example of a reflex arcs is the pain-withdrawal reflex. Although the sensory stimulus triggering the reflex arc may also trigger the HPA axis, the basic circuitry of a reflex arc does not include the HPA axis. The pain-withdrawal reflex, for example, is basically designed to jerk a limb away as fast as possible in the presence of acute pain as a protective mechanism.