In the actual military the untoward influence (real or perceived) of the convening officer on the outcome of the case is a B.F.D., just witness all the sexual assault/harassment cases that were being upended by Obama's condemnation of servicemembers who engage in them. In fact SECDEF himself had to issue a memo saying, in effect, that the POTUS expects trial members/judges to use their own independent judgment when considering the facts of a case, just as specified in the M.C.M.
You're right that an independent actor is what is needed in general, but Col. Lind does not report to the President on this, she reports to the Commanding General of the Military District of Washington, which is a completely separate chain of command from the one that was issuing orders relating actions in Iraq of Afghanistan.
Passing the laws is not being part of the process of applying them (its also inaccurate to say that the UCMJ is "set out by Congress, not the President", since the current version of the UCMJ wasn't adopted over a Presidential veto.)
> Likewise the trials are overseen in the end by the civilian Supreme Court.
Which, given the length (both procedurally and temporally) of the appeal chain is a far more distant involvement of a non-executive actor than is the case in civilian trials.
> You're right that an independent actor is what is needed in general, but Col. Lind does not report to the President on this, she reports to the Commanding General of the Military District of Washington
The existence of intervening steps on the chain of command does not make a military officer independent of the Commander-in-Chief.
The chain of command issuing the unlawful orders and participating in the coverups is unlikely to agree that revealing those things is in the "public interest".
Which is kind of the fundamental problems that whistleblowers always face (whether or not formal protections are in place) -- the people deciding whether or not to punish them (or whether or not the protections apply) are often the people on whom they are "blowing the whistle", or at least people with shared interest with the targets of the whistleblowing.
This is mitigated when there is involvement of an independent actor in the process, but in the case of military trials that are completely within the military chain of command within the executive branch, that kind of independence is hard to find.