Did you read the sicha I linked to in this post? The analysis refers to טמאים ביד טהורים רשעים ביד צדיקים וזדים ביד עוסקי תורתך. I don't think that is unique to the Alter Rebbe's nusach.
A little study of history seems to confirm this, almost like the Russian communists weren't so bad to Yiddishkeit if not for the Yevsektsya (which was comprised of Yidden), so to the Syrian Greeks didn't really care that much about what the Yiddishe spiritual life was all about, as long as taxes were paid, it was the מתיוונים that brought about the גזירות against yiddishkeit.
I hadn't seen the link earlier, but just looked through it. Far be it from me to tell anyone how to learn up a sicha, but it seems clear to me that his chidush is that in addition to the war against the yivanim, there was a nitzachon over the misyavnim. but clearly the gezeiros were coming from the yevanim, he says that explicitly, and it's quite clear from the sicha that's who the war was with as well. What I was saying was that if we understand, as per the sicha, that there was a strong element of hodah for the nitachon over the misyavnim, who were on the side of the greeks, it makes sense that we don't specifically than Hashem for the war, because Jew vs Jew is never desirable.
However, if it was purely Jew vs Greek, as is the conventional and simple understanding in the world I grew up in, then there is an element of hodah for the actual war, because of strengthening of bitachon.