XXVI. Of the Unworthiness of the Ministers, which hinders not the effect of the Sacrament
Although in the visible Church the evil be ever mingled with the good, and sometimes the evil have chief authority in the Ministration of the Word and Sacraments, yet forasmuch as they do not the same in their own name, but in Christ's, and do minister by his commission and authority, we may use their ministry, both in hearing the Word of God, and in receiving of the Sacraments. Neither is the effect of Christ's ordinance taken away by their wickedness, nor the grace of God's gifts diminished from such as by faith and rightly do receive the Sacraments ministered unto them; which be effectual, because of Christ's institution and promise, although they be ministered by evil then.
Nevertheless, it appertaineth to the discipline of the Church, that inquire be made of evil Ministers, and that they be accused by those that have knowledge of their offences; and finally being found guilty, by just judgement be deposed.
This article is fairly standard Augustinian fare. St. Augustine wrote extensively concerning the Donatist controvery. In a nutshell, the Donatists were a separatist sect in the 4th Century that were reacting against those Christian ministers in the Church that had been traditors. Basically a traditor was a Christian who, during the Persecutions, had apostasized the faith in some way. Usually, this involved flat out public renunciation of Christ and the Church. However, sometimes Christians were labelled as traditors even if all they did was burn a little incense to the Emperor, which other Christians perceived as idol worship and therefore forbidden.
Other Christians might also fudge the issue a bit when Roman soldiers showed up to their doorstep to demand copies of the Bible or other Christian sacred objects to be destroyed. Christians were suppose to hid such things and resist. Some Christians would turn over sacred objects or parts of them if they thought the Roman soldiers would leave them alone. Sometimes Christians would turn over documents that were not even religious in nature and simply say they were the bible. Romans who did not speak Greek or Hebrew would not know the difference. But, regardless of the degree of the apostasy, many Christians after the Persecutions had blown over recant their apostasy and become ministers again after some public penance or some such thing.
The Donatists wanted nothing to do with apostates. Once you apostasized in their view, you commented the unforgivable sin and should never be allowed to be Christian minister again under any circumstances. Those that did were viewed as purveying invalid sacraments. In a fit of almost Puritanical rage, the Donatists broke off and tried to form their own true church.
Saint Augustine thought this was nonsense. He argued convincingly that the validity of the sacrament was not contingent on the moral validity of the priest. Otherwise, we can never truly know what sacraments are valid and which were not, as all priests sin. We have to assume that God's grace overcomes the moral faults of His ministers.
Certainly priests and bishops were known to be corrupt from the Middle Ages on, which was one of the major cries of Reform for the Protestants. The English Reformation did not purge corruption or sinful priests. In some ways, just the opposite occurred, as they became ingratiated to the King and Parliament for their benefices. This Article of Religion is basically following St. Augustine's lead on this issue.
I agree with St. Augustine and this Article for the theological reasons I have already summarized. As this article also notes, this does not excuse sinful behavior from ministers. They are still responsible for their actions and if they do not repent, they should be removed from their office. Priests are fallible, but God's grace is still found in the Sacraments administer by such ministers because the Sacraments are God's and not Man's.