I feel like the public's knowledge of the mushroom war is severely lacking.
Firstly, I should note that as an employee of the Department of History, Ice Kingdom Division, my education has been subject to some unfair biases in available source material (The no trespassing law has kept us from excavating a number of promising locales that, should we get the go-ahead, would provide a dearth of previously forgotten information.
However, from my research, it's pretty clear that the Candy Kingdom historians have brushed aside key historical facts in their pursuit of fabrication of a history favourable to furthering their own plans.
Primarily, one has to understand that the Land of Ooo does in fact exist. You'll notice on the maps that the island vaguely resembles Australia. Well, this isn't just a coincidence, but in reality the Land of Ooo is the future state of the Australian micro-continent. Shortly after the start of the Great War, October 23rd, 2077, with China and the US locked into nuclear warfare for two hours, most of mainland Asia and North America were destroyed by nuclear explosions.
One of the most forgotten parts of the Great War of course, are the American misfires that hit Australia and Japan. Originally targeting Shanghai, the warheads appear to have been blown off course by wind, storms, or possibly a drunk man at the controls. Eighteen nuclear warheads were confirmed to hit Australia, with nine of them hitting the north-western coast (This created a nuclear winter, giving birth to the Ice Kingdom).
The resulting nuclear radiation over the next century would lead to Australians mutating and surviving, although their language would be damaged severely, to the point that Australia had linguistically devolved to "Ooo".
Mind you, in the West they lost all known information about Australia, as they were distracted by the reveal of the Vaults and the adventures of the Lone Wanderer and other Vault survivors. This is why you see little to no information about Ooo in Western historical pieces.
Source: The History of Ooo: Of Kangaroos and Candy - Gunter
edit: It was the 23rd of October, not the 22nd. A Saturday, if memory serves.