Is “Emperor Huizong of Song often left the palace incognito to secretly meet the famous courtesan Li Shishi, and Song Jiang used this channel to successfully seek amnesty.” true?

Emperor Huizong of Song, Zhao Ji, was indeed a romantic sovereign, and rumors of his favor toward the famed courtesan Li Shishi are widely found in Southern Song unofficial historical notes such as the "Waizhuan of Li Shishi" (《李师师外传》), but the official dynastic history "Songshi: Annals of Emperor Huizong" (《宋史·徽宗本纪》) makes no mention of this. In chapter 73 of the novel "Water Margin" (《水浒传》), Li Kui is quoted as saying that Song Jiang "went to the Eastern Capital to keep Li Shishi, which is a great example." As for the plot in the novel describing Song Jiang, Yan Qing, and others sneaking into Bianliang, the Eastern Capital, bribing Li Shishi heavily, and thereby meeting Emperor Huizong to submit a petition for amnesty, it is purely a figment of imagination. The real uprising was suppressed by Zhang Shuye, and there is absolutely no historical fact of seeking amnesty through the back door of a courtesan.