The question is what would be the aerodynamics behind the full back stick recommendation?
In the jet aircraft that I've 'spun' (spinated??), both the T-37 and T-33, and the others that I haven't, the initial stick full aft advice was to assure you weren't in an inverted spin before other recovery inputs were applied. In an inverted spin in the aircraft I'm familiar with, stick full aft will result in transition to an upright spin. From there you're dealing with a known quantity, inverted spins can be very disorienting, uncomfortable and difficult to assess. Intentional inverted spins in the T-6 are prohibited for this reason, not because they're unrecoverable.
T-37 recovery was essentially the same as the A-5 procedure and was, of course, taught regularly in USAF training because the habit patterns carried over to fighter aircraft of the time. Nowadays you just let the FBW take care of you.
BTW, probability of recovery in the A-5 sounds about the same as that of an F-100F.