Saying “key decision-making authorities” sounds like exactly that: key positions. Moving key existing positions out of conflict of interest.
To finish your quote:
He said he didn’t “want to bore you with detail here,” but that basically, “this change required a completely different shift in the way these crimes are investigated and prosecuted by taking them outside the chain of command, which already had existing protocols in place in existing judicial system.”
That really explains it, I don’t know why you cut it off.
“I know it may not sound like much,” Kirby said, “but it’s a big change to the way the military did it.”