Is “Ehuang and Nüying throwing themselves into the Xiang River out of love” true?

According to folk legend, Emperor Shun died in Cangwu, and his consorts Ehuang and Nüying's tears formed 'speckled bamboo' as they wept, before they threw themselves into the Xiang River and became goddesses of the Xiang River. Although the 'Xiang Lady' was already eulogized in the 'Songs of Chu', the 'Records of the Grand Historian: Annals of the Five Emperors' only records: 「践帝位三十九年，南巡狩，崩于苍梧之野。」 and does not mention the two women throwing themselves into the river. The claim of their suicide for love finds no basis in early classical texts and was gradually fabricated by later literature.