One of the reasons that Chan Jen Nam was so loyal to the Cheng Family of Taiwan (Coxinga and his descendants) was his belief that, absent a legitimate descendant of the Chu royal family of the Ming Dynasty, the Kingdom of Tungning was the closest thing to a legitimate heir to the old Ming Dynasty.
Chan Jen Nam, however, never met the One-Armed Nun, who was in fact Princess Chang Ping of the Ming Dynasty. By the time of her appearance in DOMD, Princess Chang Ping was likely the last survivor of the Chu royal family. If Chan Jen Nam knew of her existence, would his loyalty (and that of his Heaven and Earth Society) have gone to her instead? As an actual blood descendant of the Chus, Princess Chang Ping had a more legitimate claim to the Ming throne than the Chengs did.