I struggle to understand why the Pentagon is muzzling military chaplains as they try to counsel soldiers for stress but is moving forward at light speed with eastern religion based therapies.

The linked HT and GI study used a very weak standard for PTSD. Only one PTSD symptoms qualified the subject for the study. The relaxation skills taught in the Guided Imagery overlaps with simple relaxation skills. Single symptom PTSD would easily be responsive to learning relaxation and the CBT skills taught.

This sounds similar to the study the ImPACT people did that lead them to believe that a second concussion does not cause any more symptoms that a single concussion. If one reads the details of the study, they see the disclaimer that the ImPACT system may not be sensitive enough to measure a difference.

As was said long ago:

There are three kinds of lies,
lies,
damn lies, and
statistics.

YMMV

Your Mileage May Vary.