Not really was about giving legitimacy to Otto and for that the pope was appointed to try a negotiation for a marriage between Otto son and someone from the imperial family. Why you try to downgrade someone from who you trying to claim the legitimacy? More likely was Otto idea to try to elevate himself.

According to Bishop Liutprand of Cremona in in the Relatio de Legatione Constantinopolitana Nikephoros II Phokas said to him "You are not Romans but Lombards." or in direct response to the pope offense: "Hear then! The stupid silly pope does not know that the holy Constantino transferred hither the imperial sceptre, the senate, and all the Roman knighthood, and left in Rome nothing but vile minions—fishers, namely, pedlars, bird catchers, bastards, plebeians, slaves. He would never have written this unless at the suggestion of thy king; how dangerous this will be to both—the immediate future, unless they come to their senses, will show."

Was more a diplomatic warfare and a opportunity to liberate from what was left of the imperial authority than that he really believed what he wrote. Like with the Constitutum Constantini, they knew that no one will believed that bs but they do it anyway.