That is the point of the ICC in the first place: you cannot trust the war criminals to bring justice to their society.
We might be able to trust countries to judge their soldiers' behavior when these soldiers act on their own. The problem, and the reason, I believe, why the US won't voluntarily accept the ICC is when they don't, e.g. when drone operators bomb a wedding reception, because it's not going to be those individual operators on the hook - it's the mission and the larger policy that are going to be implicated. And a military doesn't want their officers to ask themselves "wait, can I do this? Will I be prosecuted for this?" when told to do something, they want them to say "Sir, yes, Sir" and mean it.
And were they brought to justice and sentenced for their crimes? No. A sham trial isn't sufficient for war crimes.
The worst of the worst war crimes will be prosecuted in the US as well, but generally, soldiers have little to fear. A non-US court wouldn't have the same perspective.
Essentially: if you want people to do whatever it takes to get your mission done, make sure they're not liable for anything they break while doing so. That goes for the military as much as for tech companies. Tech companies just don't have armies to back up their stances, yet.