Is “Fought with the Yellow Emperor at Banquan” true?

The Records of the Grand Historian, 'Annals of the Five Emperors', records in detail the war between the Yellow Emperor and the Flame Emperor: 'The Flame Emperor wanted to encroach upon the feudal lords, and the lords all turned to Xuanyuan. Xuanyuan then cultivated virtue and strengthened his troops, regulated the five vapours, planted the five grains, comforted the myriad people, surveyed the four quarters, and trained bears, brown bears, pixiu, chu and tigers, and with them fought the Flame Emperor in the wilds of Banquan. After three battles, he then achieved his aim.' This Battle of Banquan, which determined the formation of the Chinese nation, is described with a high degree of consistency in historical documents.