Converting Bad Into Good

The Gemara (Gittin 57b) says that Na’aman (commander of the armies of Aram) became a ger toshav; Nevuzaradan became a ger tzedek; Haman’s descendants learned Torah in Bnei Brak; Sisera’s descendants taught children in Yerushalayim; and Sancheriv’s descendants taught Torah publicly.
The Gemara only identifies the descendants of Sancheriv. They were the great sages Shmaya and Avtalyon. The Rambam seemingly writes that Shmaya and Avtalyon were proselytes themselves, not merely descendants from converts. Yet the Gemara says that one of them became the nasi and the other became the head of beis din. The Magen Avos says that if the Rambam is correct, then those appointments were a violation of the rule that positions of authority cannot be assigned to converts. The Maharal therefore explains that Shmaya and Avtalyon had one Jewish parent and were not considered full gerim.
The Magen Avos disagrees. He explains that there were no greater sages in Klal Yisrael than Shmaya and Avtalyon. While it is true that positions of authority should normally be given to natural-born Jews, that applies only when they are equally qualified. Shmaya and Avtalyon, although converts, surpassed all of their Jewish peers in scholarship. No alternative candidate equal to their stature could be found. Hence, they were appointed to be the nasi and head of the rabbinical court.