Many Baptist churches would not accept Presbyterian baptisms for various reasons, including that they are mostly administered by sprinkling. That would be my position. Some groups, like the Free Presbyterians (Ian Paisley) baptize by immersion as well as sprinkling, but such a church would not be regarded by strict Baptists as being of "like faith and practice" since immersion is optional, so they would not accept immersions from such a group.
Yes, Renegade, you are correct that most of us strict fundies would accept an immersion by an administrator who turned out to be unsaved, as long as that administrator was duly authorized by a church of like faith and practice. In that regard, we are in agreement with the Roman Catholic position on that issue, as opposed to the Donatists in that controversy which goes back to the 4th Century in North Africa.
Going back to the RC baptisms in Arizona that were declared to be null and void, that brings up an interesting point. According to RC doctrine, infants are saved, regenerated, born again, whatever we call it, as a result of a valid, properly administered infant baptism. However, no RC church member can be sure that his/her baptism was valid, with the priest using the proper verbiage. If the priest stumbled over the words and got it wrong, then the baptism was invalid and the "baptizand" was not saved!!! The improperly baptized church members in Arizona were invited to seek proper baptism and get it right, but what if some of them died before they had the chance to get it taken care of? According to RC doctrine, they must have gone to hell. OOPS!
Not only that, but according to RC doctrine, the priest must have the proper "intention" when performing the baptism, or else it is not valid. How does that baby know, after he grows up, that his baptism was valid and that he is saved? There is no way for him to know that. Cardinal Bellarmine said, "No one can be certain, with the certainty of faith, that he has received a true sacrament, since no sacrament is performed without the intention of the ministers, and no one can see the intention of another." (Works, Volume I, p. 488)
Former RC priest Joseph Zacchello wrote, "This teaching implies that no Roman Catholic, be he priest or laymen, can ever be sure that he has been properly baptized, confirmed, absolved in confession, married, received holy communion or extreme unction. . . .
"Suppose a child is baptized by a priest who lacks the proper intention. The baptism is then of no avail, and the child grows up a pagan. If he should enter a seminary and be ordained a priest, his ordination will be invalid. All the thousands of masses he says, all the sacraments he performs, will likewise be invalid.
"If he becomes a bishop, the priests he ordains and the other bishops he consecrates will have no such power. If by chance he should become pope, the Roman Catholic Church would then have as 'Vicar of Christ' and 'infallible' head a man who was not even a Christian to start with!"
(Secrets of Romanism, p. 110)