Pfft
I'd be ultra-surprised if any military *bothered* to try to decrypt it, even if they believed it to be damning. If it's damning, they KNOW what it is, know who COULD have it and know who's likely to be the source. They wouldn't need to "verify" it at all.
And wasting billions of CPU cycles just to say "Oh, yes, those are the classified files" (to yourself) is a bit pointless - if you suspect they are, you have to ASSUME they are, and work from that assumption. Note that this doesn't mean confirming they are authentic in a public forum under any circumstances - any military that did that is too stupid to manage its own PR team - confirmation or denial is as good as authenticating and thus "approving" the collection, content of, and dissemination of all that data publicly. Oh, and if they are, then they are now "compromised" so it pretty much doesn't matter if one person or a million saw them - thus you only have to worry about the consequences and methods of leak rather than the actual particular leak itself.
If you know for sure they are not your files, well, it would be easy to call them on it, make them give you the key for verification purposes (there's no point paying a hostage-taker when you're not sure he *HAS* any hostages) and a 0.001 second decryption of the first few bytes with the key they give you to see if they do have something you didn't know they had. Or you could just ignore it and let them make a fool of themselves.
The best thing for ANY military intelligence organisation to do is absolutely nothing until it becomes a militarily-important operation - and then you've nothing to lose by just blowing everyone away whether they're in a foreign country or not. If they are genuinely going to compromise your military, blowing them away is the best option no matter what kill-switches, colleagues, etc. they claim to have. If it's that big a problem, blow them away too. It's a military leak, not a kindergarten rumour.
I don't think the US public would hate you at the moment if you were to say that he was threatening to release some much-more-sensitive information that would compromise military installations, special forces, "our boys' lives" and so you took him out. Even if it's against some law or constitution, there are countries willing to do your dirty work for you (isn't the UK special forces arm basically used for assassination of people that the US doesn't like because they have a law about doing that and we don't?).
In all the movie plot threats, yes, the security services might try desperately to decrypt these files. More likely or not, they hardly know they exist until you try to publish something that's actually damaging to the military in a non-PR way (Does a military really care about PR? They kill people for a living!) - like operationally-important details - and then they just kill you. It's like the XKCD cartoon - do you spend years trying to decrypt ultimate mathematics, or do you just hit the bloke over the head until he gives you the password and/or takes the password with him to the grave?
Hell, the US tortured foreign people, in foreign countries, totally against all its own laws and even allowed filming, photographs and non-classified, bog-standard, low-ranking Army personnel to do it. Do you really think they'd care a jot about just taking someone they consider an *actual* military threat (not a PR threat), torturing him using the same Special Forces personnel that could be put in danger by his actions, and then doing everything under the sun to him until he dies / tells what he knows?