And, of course, thanks to everybody else for their thoughtful responses as well! 
King has no problem with a deus ex machina as long as it’s on the side of good. His stories are replete with examples of the bad guy (or the Dionysian influence, as he once put it) having all the cards stacked in his favor, and some incredible coincidence or bit of luck allowing the good guy(s) to restore the proper Apollonian order to things.
As Gandalf said to Frodo in Lord of the Rings (paraphrased), “You were meant to have the Ring. There are other forces at work here, and not all of them are on the side of evil.” I think this is King’s basic approach to storytelling.