This is not so much a lie as an over-simplification. Anyone suggesting that the US did not play a major role in WW2 is foolish.

I'm sure that as a thought exercise, someone could identify a number of different events or courses of action in WW2 which could have in principle changed the outcome of the war. In that sense, there are many things which "won" WWII.

Further, number of casualties is a perfectly fine argument for "who sacrificed the most," but not necessarily for who "won" the war.