Well, “P because Q” doesn’t actually entail that “If it weren’t the case that Q, it wouldn’t be the case that P.” There are cases where one cause trumps another cause that would have been sufficient had the trumping cause not been present: where if Q hadn’t caused P, something else would have.
Example: A is going on a three-day expedition deep into the desert. B wants to kill A, so B secretly poisons the water in A’s canteen. C also wants to kill A, but doesn’t know that B poisoned the canteen, so C drains all the water out of the canteen. A dies in the desert of dehydration; A was killed because C drained the canteen. But it’s still true that even if C hadn’t drained the canteen, A would still have been killed: she just would have been killed by the poisoned water instead of by dehyrdation.
This could also be the case in terms of war justifications. (You might think that there’s a secondary reason that would be sufficient, even if the primary reason turned out not to be sufficient after all.) But of course you’re right that most people argue in the way you have in mind are just making excuses for a predetermined policy, so just about anything at all would do. In that case you’re right that the “because” hasn’t been earned.