The people were baptized by a priest. Questioning wheter of not it was valid paralells a movement called Donatism. Look it up.
Well, mgy, I trust this has been clarified for you, but again it is the form of the administration of the sacrament for validity that would be at question. It pertains to the supreme authority of the Church to define what is needed for their validity (canon 841). Judgement in a particular case of whether those elements were present would normally belong to the diocesan bishop.
Again, the point is that there can be no separation of persons in regard to who pronounces the proper form of words and performs the washing with true water. The worthiness of the minister is entirely a moot point.
However the intention to baptize is required, and is presumed. But if the minister had no such intention, such as an actor in a movie going through the motions and saying the words, there would be no baptism.
Similar issues of validity would be raised if the minister used an improper form of the Trinitarian formula (e.g., baptism in the name of the Creator, Redeemer, and Santifier) or so called “Jesus’ name” baptism, or substituted perfume for true water.
Do keep in mind that the Church does define the matter and form for the validity of sacraments. It does pass judgement on whether sacraments were validly conferred since there are spiritual and canonical implications. Examples that come to mind most obviously are matrimony (though non sacramental marriages can also be examined) and rarely, ordination. Sometimes these boards contain questions about the validity of sacramental absolutions as well, and those threads can be read.