Anna and Austin are correct: many people lived on ranchos, labores or haciendas, far from the town center, and because of the distances, clerics could not always be summoned in time. That’s why you’ll see on some burial records that the deceased didn’t receive last rites, “because of the suddenness of the illness.” In the case of newborns in danger of dying (“en caso de necesidad,” or “in articulo mortis”), if there wasn’t time to summon a priest, a lay person could perform an “emergency baptism,” who would’ve sprinkled holy water (“echar el agua”) and recited the correct biblical passages. If the child survived, the person who performed the baptism would be reviewed, to verify that he was a “capable person, and who knows the material and ways of this sacrament.” I suppose the baptism would later be completed, as the priest still had to anoint the child with “Santos Olios y Chrisma.”

I thought perhaps only pre-approved laypeople could perform these - I have an ancestor who owned an hacienda, and he performed several, and another who was a mayordomo on an hacienda, who also did several, but I also had an ancestor who was neither, yet he once baptized a child “in articulo mortis” in his own home (on the same day his own child was baptized "in articulo mortis" in the home of the mayordomo!).

Chao,
Manny Diez Hermosillo