I know of one person who had a difficult life, prayed for help, got the knock at the door, got baptized ....
I was exposed to the JW religion as a child, but my mother was disfellowshipped when I was just a kid (because the end of the world didn't come). She went back, I did not. I got into "a difficult life, prayed for help." That's a nice short version. (If you want the long one, let me know in a PM.)
It wasn't a knock on the door. Instead, my JW mother sent word through the organization that I was in a military hospital and two brothers called on me there.
We can jump to "....got baptized ...." I think the point you are focusing on is that this was supposedly an answer to my prayers, but your example and mine would contradict that answer by leaving the Witnesses.
......and eventually left the JWs believing they were a cult.
Has this happened to any of you? And if so, did you still feel your prayers were answered at that time?
So I eventually figured out that Watchtower is a dangerous mind-control cult. It would be easy for me to say "There was no God involved in the first place, so no prayers answered at first nor later." But for the likes of Perry and others, let me say this:
I was primed for whatever the reality of God was, whatever the beliefs. If God was Allah or the deity of any Christian denomination or something outside of all religion, I was ready to follow His/Her/It's/Their path for me. I begged for God's intervention and enlightenment in my life. If God wanted me, I was ready. If God allowed me to be sucked into the Jehovah's Witnesses at such a point in my life, then he's a dirty dog. He's wasted my decades and I ain't going to waste them with Him anymore.
Of course, I know better. Psychology can fully explain what happened to me and science can amply demonstrate that man invented the gods. No gods involved.