At this point I had decided that I wasn't going to hang around the basilica, so instead I started back down the Via Frate Elia to look around the town a bit more.
The Via Frate Elia is named (I believe) after Friar Elia da Cortona, aka Elia da Assisi, who was born as Elias Bonusbaro (Buonbarone) (1178 - 1253). A lawyer by trade, he became one of St Francis' earliest followers and was given many diplomatic assignments. He was close to the Holy Roman Empire in general and King Frederick II of Swabia in particular, and tried to reconcile the Holy Roman Empire with the Catholic Church. This resulted in him being excommunicated in 1240. Though according to some versions of his history, he did considerably more than state the emperor's case, rather actively taking up arms against the Papal factions.
According to the English version of Wikipedia, he was not in fact a priest or a cleric but rather a lay brother who was important for his organisational skills. I think that may be questionable given some of his roles and the fact that the street name includes the title "Frate", but it's not impossible. Apparently he was the original architect of the basilica that the Pope had decided to raise after Francis's death.
It was not until after the death of King Frederick II 10 years later that he was reconciled to the church.