*laughs* Swain seems to be getting himself in much more trouble then Jarvin has ever been in. Starting a war without the leagues permission over silly mining rights I'm sure they could just ask one of there many allies for help oh wait they don't have any. But you did name one hero who hasn't been brought back to life and is viewed a hero, but I'm sure after all this is over that will change.
One; the Demacian turncoat was likely honor killed by his own people to hide his stain of treason.
Two; Grand General Boram Darkwill, the Noxian equivalent to Jarvan III, was assassinated and all fingers point to Demacia as they hold the only force capable of ambushing an entire platoon of Raedsel Guardsmen and the only people other than Ionia with motive to do so.
Three; Jarvan IV threw the first punch against Swain in broad daylight in his own camp completely unprovoked not long after Darkwill was assassinated. Furthermore, Noxus has vowed not to unleash any unsanctioned magics in the defense of their people so I hardly see how the league can take issue.
Noxus didn't start this war, but she will finish it.