It is not a matter of being dependent upon a priest or the priest’s perfection. Technically, anyone can baptize. We cannot baptize ourselves; someone else must do it for us. (A sort of sacramentally reinforced anti-Pelagianism, I suppose.) If we were baptized in an improper manner, we are not in the Church, and must be rebaptized. That is the apostolic practice, as recorded in the Book of Acts.