FDR and Truman(both Dems) would outright censor if not completely shutdown and/or arrest people for lying like this while WW 2 was happening. . .as far as I know a president was never stripped of that power even if it's a razor's edge between free speech and worse.
Military action is different from war. We can send troops to a country to fight troops from other countries, but if there is no declaration of war, then it is not a war