I understand this.  I am questioning whether the HL technique has any predictive value at all.  If it didn't predict Cantrell's peak, why would the technique suddenly become predictive immediately following the peak?

While I like the elegance and simplicity of the method, the shown fits do not convince me of its utility.

why would the technique suddenly become predictive immediately following the peak?
I see two main reasons:
  • we know that a fast and terminal decline is expected (see the official chart on Fig. 8).
  • the predicted URR (17 Gb) is close to the official number (20.5 Gb)

I could have used something else that a logistic curve: a gaussian or a constant R/P ratio used by economist. Any monotonic curve that is delimiting an area close to 9 Gb will have done the job.
Is there any reason to believe then that the HL method is better model than, for example, eyeballing the decline (based on the two post-peak points) and calculating the area under the graph to generate a URR figure?
You can find some background on the logistic model applied to the modeling of ressource depletion in the following post:

Links to tutorial material on Hubbert Linearization

It seems to work but no one knows why. I have a problem with understanding what the logistics K physically means. I think the real depletion rate for all Mexico is under 10% of available reserves using a more realistic rate model.

http://mobjectivist.blogspot.com/2006/03/mexico-oil-shock-model-part-2.html

Again, I don't think K makes any real physical sense.