I am not sure how this relates to the papal infallibility. Leo the Great's letter was simply "orthodox" in the sense that he held fast to the previous teachings of the Church.
The bishops proclaimed that they believe what Leo believes. One could say that he believed what they believed by reciprocity. They didn't beliebe because he believed. He did not legislate that belief.
But since we are on the subject of Chalcedon, the very same bishops who wholeheartedly agreed with Leo's theology also wholeheartedly disagreed with the scope of his idea of papal jurisdiction (Canon XXVIII).
The fact that Leo's letter was read aloud at Chalcedon has a lot to do with the fact that the Bishop of Constantinople was Leo's appointee and that Leo in no uncertain terms expected that the Bishop of Constantinople ought to "behave."
Only 20 years earlier (under a different Ecumenical Patriarch), Leo's Tome was not read. In fact it was wholeheartedly . The Council of Ephesus, which Leo didn't recognize as ecumenical (papal legates arrived late and the Council was in no mood to wait for them!). Nonetheless, Leo's successors acknowledged the Council of Ephesus as an Ecumenical Council, and likewise acknowledged the disputed canon XXVIII of the Council of Chalcedon.
Clearly, the office of the pope did not have the same meaning to the Church as did after the Great Schism and as it does today. It was Leo who initiated the theory of Petrine supremacy, based on his NT interpretations. In fact the first Bishop of Rome to even assume the title of the Pope was Siricius (384-399), who died only a year before Leo was born (400).
Papal legates at Chalcedon even went as far as to arrogate for the Pope Leo the title of "ruler of the church." The response of the bishops made it clear that that they didn't think so. Even the Illyrian bishops, who were brought into Leo's hold only a few years earlier, sided with the Council and the Emperor.
Leo's lamentations to the Empress and the Emperor, as well as rather unveiled threats against the Bishop of Constantinople, were ignored by the Church and the Emperor. His veto of the Canon XXVIII was also wholeheartedly ignored, indicating that no one really considered him the "ruler of the Church." as a whole, despite some individual fathers expressing private opinion to that effect.
The idea of a supreme papacy, the idea of imperial papacy, is something that developed in time and was not in place in the Church at the beginning, and for the next five centuries thereafter.
The relation is that Leo the Great made an ex-cathedra pronouncement before the consensus of the bishops was reached, and over time the consensus followed. This was a de-facto exercise of the only contorversial aspect of papal infallibility: that the pope may promulgate doctrine not waiting for the consensus.