A Voice from the Past - Nicolas I

(In response to whether baptism given by a man pretending to be a priest is valid.)

If baptism comes unimpaired to the person receiving the gift, even though it was given by an adulterer or a thief, why does it not therefore stand unimpaired and without need of repetition when some worldly fellow, pretending for I do not know what reason to be a priest, has offered it?

Nicolas I, 820-867 AD, Answers to the Questions of the Bulgars, Chapter XV (translated by W. L, North, MGH Epistolae VI, edition of Ernest Pearls, 1925, Letter 99, from Internet History Sourcebooks, Medieval Sourcebook)

What is the validity of the ordinances based on? Does it matter who administers them?