There is a Miyashogun (shogun from the Imperial Court) theory that says he was enthroned as a Tokugawa Shogun by Tairo (chief minister) Tadakiyo SAKAI when the 4th Shogun Tokugawa Ietsuna died without an heir in 1680 (=> see "Problem of heir of Shogun," a case where a shogun died before the decision of an heir).
延宝8年（1680年）に将軍徳川家綱が継嗣のないまま死去した際に、大老酒井忠清に徳川将軍に擁立されたとする宮将軍擁立説がある（→将軍継嗣問題継嗣決定前に将軍が死去したケースを参照）。