Steven Taylor debunks the theory that the Saudis didn’t care about saving Paul Johnson:

It seems that with the scant information available, that the logical conclusion is that something about the disposal of the body or the delivery of the video tipped off the Saudi security forces leading to al-Moqrin’s whereabouts and his subsequent death.

An alternative conclusion is that killing al-Moqrin would have pretty much guaranteed that Johnson would be executed; thus, the sensible course of action was to wait until after they confirmed Johnson was dead to go after al-Moqrin (who may not have been at the same physical location as Johnson anyway).