While you're right that proof won't be forthcoming from military hospitals, those reasons aren't quite right.
At smaller, low volume military hospitals the patient acuity and case complexity is indeed very low - think of a surgicenter with better screening than most.
But the majority of patients at the larger military hospitals are retirees and family members of active duty personnel. I'd guess 80%+ of our patients are NOT active duty military. Retirees and family members are not covered by Feres Doctrine; they can and do sue. The retirees can be very unhealthy. These hospitals do neurosurgery, pump cases, complicated OB with NICUs and the associated neonatal OR trips, etc.
The reason CRNAs aren't bumping off patients left and right at military hospitals isn't because there are no sick patients; it's because the sick patients are done by anesthesiologists, and the CRNAs aren't really practicing independently. The daily assignments are made by an anesthesiologist and cases are triaged so that sick patients and complex cases go to an anesthesiologist (+/- a resident). CRNAs are required to consult with an anesthesiologist for ASA 3+ patients ... though in truth 90%+ of the ASA 3 patients they see are elective total joints who get blocks from an anesthesiologist followed by a spinal, ie soft ASA 3s.
Additionally, military CRNAs are, on average, substantially better than civilian trained ones. Their training is better; they get better candidates in the first place; and SRNAs don't pay tuition so they can be failed and kicked out of the program if they do poorly.