The little lantern boy mentioned, "the battle between Mount Oe and humans" should refer to Minamoto no Yorimitsu's expedition against Mount Oe.
So, it can basically be determined that the legendary human-demon war really existed.
According to what the Countermeasures Office said, during the Heian period when Mount Oe's forces were active, Japan was a time of human-demon coexistence.
It is speculated that the active stage of humans and demons was in the Present World, or perhaps, unlike now, the Present World and Tokoyo were not so distinctly separated. During that era, there might have been a more convenient way for the two worlds to communicate with each other.
Perhaps it was precisely because of Mount Oe's presence in the Present World, which endangered Kyoto in the human world at that time, that a conflict broke out with the Minamoto clan, which defended humans.