Except, there was no spinal injury found in the autopsy, so there would be nothing to trigger that reflex. Yet, we do know he had a wound in the front of his neck exactly where he seems to be grasping. Grasping at such a wound, which probably interfered with his breathing, is also a perfectly natural reaction, and fits the facts better than a reaction to a non-existent spinal injury.
The bullet strike from the second bullet fired by Oswald (also causing Connally's wounds) was located near the center of JFK's upper back, high between the shoulder blades. The Thorburn Position doesn't require that the spinal cord actually be pierced or cut; just sufficient regional trauma to the lower cervical area is enough to exhibit the symptom. This was a high velocity rifle bullet wound, and as such the traumatized tissues are many times the diameter of the actual projectile circumference.
Moreover, place your finger at the spot on the front of your neck where you'd imagine the top of your necktie to be located then imagine drawing an invisible line straight through to your back. That spot is fairly low down between your shoulder blades, isn't it? The wound Kennedy suffered was significantly higher, thereby demonstrating evidence of a downward path of the bullet trajectory as fired from the TSBD sniper's nest.
There was no spinal injury-—the neck wound was a clean flesh wound and survivable, but when the bullet went through, there was a lot of blood that suddenly started flowing down his throat and windpipe-—he in fact could have drowned in his own blood.