Hi Bob,
Now your getting into my "day" job.
The "New Rules" has its title wrong. Those are the "old rules".
And your chiro, while trying to be helpful, is a little off the mark too.
The idea is not to strengthen the legs, or really any specific bodypart. The idea is that they all must function in an integrated, balanced and functional way.
To continue to strengthen the legs, or any specific group, while letting the Torso/Back decondition will only insure that the same problem will happen over and over.
In fact it is far more important to have the torso strengthened "beyond" the capacity of the legs so that the "legs" are the limiting factor and not the deconditioned Torso Stabilization Mechanism.
So there are times when you have to start all over, and at the beginning, and this is one of them. To simply push on with the legs, and "let" the back heal will not yield a good result, since as soon as you bring the Torso back into the loop, the imbalance will cause a higher percentage chance of injury.
SO....
I know it is hard, but as soon as you are out of the "acute" (when you are relativley pain free during movement) stages, do the following:
1) Make sure and warm up the back before exercise. This IS NOT stretching!!!!.
Stretching is generally a forward flexion of the spine and this is what caused your problem in the first place. Forward flexion (bending) of the spine (especially the lumbar/low back spine) compresses the anterior portion of each lumbar disc. It also "opens" and decompresses the posterior portion. This anterior compression creates a hydraulic pressure forcing the nucleous pulposus (thick fluid like center of the disc) to exert pressure to the posterior disc walls (anular rings) and if the pressure is great enough it cause a distortion or bulging to the disc that can push into the posterior lateral (rear side) nerve canal and you are in deep doo doo

2) You must start all over, and develop the "flexibility" needed to hit the bottom portion of the DL and SQT without the lower back losing a rather tight and slight arch.
As soon as that arch moves from arch to flat undler load, you are creating BIG PROBLEMS.
3) So start with the bar only and if it is too heavy use a broomstick.
For both squats, and deadlifts, use an "exagerated" Head UP/Butt Out/Back Arched posture through every portion of the exercise except the top.
With the bar only, do a minimum of 30 reps with that perfect "exagerarated" form and DO NOT allow it to change especially at the bottom of each rep.
NEVER look down, and always keep your butt out.
Then when you feel comfortable performing the reps securely with the bar only, especially in the bottom postition, then begin adding weight, at no more than 10- 20# a week, until you are back up to where you were before the injury.
The bad news, is you can NEVER just relax, when you train heavy. The whole idea is to make the body a solid mass, from which to absorb, transmit, or create force.
Jello is a lousy force platform or conduit, solid steel is a good one.
Never forget to do at least one set of 30 with a light weight to warm up. When you decide you are beyond that, that is the day you'll discover that you aren't.
But if you focus on the Torso, rather than the legs, the legs will do just fine.
But if you focus on the legs and let the Torso get behind, you're setting up for problems.
Been there, done that.
I teach workshops on it (TSM) on occasion.