The Evils of George Walker Bush: Dying "in vain"

Let's say Bush and Congress went crazy.  Let's say we had (seemingly) concrete evidence that Canada was planning a takeover, so we invaded.  Then we find out that it was all faked up evidence (see the Niger-Uranium documents, crazy Curveball, cherry picking evidence, etc).  So, now, our military has beaten the Canadian military, their government is gone, but the whole war was a lie in the first place.  Would you pull out of Canada?  Even if that meant some of the soldiers who died for a lie die "in vain?"

Let's pretend you are a German in 1942, and, in an alternative history, Hitler dies.  Sounds great.  Even better, you get to become the new Reichschancellor, Fuhrer, et cetera.  Well, you are sane, and not a Nazi, so you want to stop the war machine your predecessor has put in motion.  Part of the reversal involves withdrawing from France.  Would you be swayed by people who say you couldn't do it, because that would mean other soldiers had died "in vain?"