In all humility, please consider the following thoughts: Christianity is all about relationships, both of the person with Christ, and of the person with other people, ...
So, the reason a sudden change can occur as you point out isn't just a paperwork issue, but what it reveals is that the relationship between the person and the Church has been corrected and renewed through the Holy Spirit as revealed through the Mysteries of the Church. That is how things can change--because now it is known that the Spirit has moved among them, instead of merely suspected or hoped for: the correction of the person's relationship to the Church has changed. This is the nature of Pentecost, which many of us will be celebrating this morning: the sudden arrival of the Spirit to form the Church changed the world in that moment, while to many others nothing visible changed other than some people wandered into the street to speak in languages they understood.
As I understand it, Cornelius was acceptable in God's sight before that was communicated to Peter, and acknowledged to the church at large.
Please do not get me wrong, I am not against authority or structure. What I am against is man judging another man by his standards (canonical or otherwise) when that soul may be in good standing with God.
I see salvation as a process. What has been revealed to a soul by God today, has also been accompanied by His grace to live out that new understanding.
What has not been revealed, the man cannot live out. If a man has accepted Christ as his Head, and gives his life to bring food and medicines to the poor, for the love of God, because in them he sees our Lord, is he not in affect the hands and feet of his head, Christ? Should we not then admit him to the Lord's table if he is in understanding of the true nature of Christ's presence in the Eucharist? Because by his actions, he had demonstrated that He knows the heart of the law, even as Cornelius, knew the heart of the law.
If hypothetically, we were to remove all the traditions that have been layered upon Christianity since that day with Cornelius, would we not have a very simple basis for consensus and therefore communion?
I believe the Baptismal rite in Orthodoxy is beautiful and worthy to be adopted by all, but does not the Lord accept the same baptism that was administered to Cornelius and his family, even though we know better that one should be baptised in the name of the Holy Trinity?
I am not saying we should throw out tradition, I am saying that we need to go back to what Christ instituted as the absolute minimum for agreement. If we refuse to do this, adding line upon line, separate cooking pots for the meats and the milk, are we not degenerating something God given into something made by man?