The attacking player just got back to me--he says he saw what I saw. He also found this other thread about the problem:
http://forum.shrapnelgames.com/showthread.php?t=34902
In that thread, dudes say what they've said in this thread, plus the additional speculation that a discrepancy in operating system between host and client can also trigger the problem.
It occurs to me that this problem could be happening very often--and we just wouldn't usually notice it, because only a few minor soldiers would have had their fates misrepresented because of it. But of course it's very obvious when a major commander dies in "reality" but not in the replay.
Anyhow, I feel better about the problem now. I'd been worried that there was a mysterious bug that killed powerful berserkers at random. That problem would be very hard to defend against! But now it appears that my powerful berserkers died correctly, and that only the replays I watched were incorrect. That problem is much easier to defend against! In fact it requires no special defense at all. Just equip your commanders so they won't die, and tolerate the fact that you sometimes won't know what they actually did do.
(Of course I'll be careful about version numbers etc., but I was already careful about that, and this still happened.)
I see what you mean Sombre, about not calling this a bug when it arises due to mod version mismatches--but if that's a way to cause this error, then the game allows you to use mismatched mods when it shouldn't. I consider THAT a bug. Of course this community has a pretty high threshold for calling things "bugs" rather than "WAD" issues or even "features". At any rate, maybe we can agree that it'd be better if the game didn't let you use mismatched versions of itself.