They maintain that they only have oversight over the DOD IG, but that means that the only entity overseeing some of the most important OIGs in the government is ANOTHER OIG, subject to the whims of whomever happens to be leading it.
As opposed to, say, ALL THE OTHER OIGs, ...
who are answerable to an entire committee comprised of IGs from across the government, which is NOT subject to any particular member's whim.
Let's put this in some perspective. An agency OIG is charged with an awesome responsibility. They are often a whistleblower's only ...
recourse, & if they reach a decision that there's nothing to see here, there's practically nothing you can do about it. Because of this, by design they are supposed to operate independently of the agencies they oversee, so they won't be captured by the subjects of their review.
In order to carry out this important & often unappealable work, it is important that they be subject to close oversight by an objective outside body. It is also mandatory that this objective outside body be charged with investigating whistleblower claims ABOUT THE OIG.
Because of this, the CIGIE Integrity Committee was set up. If you have a complaint about, say, the USDA OIG, you file it with CIGIE. Each member of the CIGIE IC is an Inspector General at a different agency, so even if one of them is lazy or disinclined to believe you, that's ...
not a fatal blow to your complaint.
If, however, you have a complaint about the Navy OIG, you file it with the DOD IG. One office run by one Inspector General. And if that one IG does not run a tight ship, well then, the Navy OIG skates free.
tl;dr Military service OIGs don't have the same level of accountability as literally every other OIG in the Executive Branch. And regardless of whether or not you like the current DOD IG, you should have a problem with this. OIGs wield awesome power. They need awesome oversight.
I'm not saying that the CIGIE IC is perfect. It's far from it. But the idea is fundamentally sound, while only having one single solitary OIG be in charge of other OIGs is a recipe for disaster.