There was a rather complex background to the establishment of the Iwai family as follows; though the first Yukitoyo was a son of Tokitsune HIRAMATSU of the Shonii Gon Chunagon (Senior Second Rank, Provisional Vice-Councilor of State) (1627 -1704), Emperor Gomizunoo and Tofukumonin allowed Yukitoyo to establish a new family in appreciation of his service in his adoptive family, Iwai no tsubone.
石井家設立が上のように複雑な経緯をたどったのは、初代・行豊は正二位・権中納言・平松時量（1627年〜1704年）を実父とするが、養子先である石井局の勤務を後水尾天皇及び東福門院がねぎらうという形で行豊に新家の創設を認めたためである。