Speaking of praying and recoveries, a couple of years ago my mom had an unspecified cancer (a swollen lymph node was removed and indicated that she had cancer elsewhere, but they never could actually find evidence of it).
My parents, especially my dad, are devout Catholics. They are also both Polish, and Dad has always been almost militantly so. He had a fairly good friend, due to his high-level involvement in Polish Scouting...a priest who later became a bishop, and had known Pope John Paul II since his seminary days. JPII, having recently gained sainthood around that time, seemed to Dad the perfect person to pray to. "Family connections" and all that.
As I said, Mom's cancer was never actually identified. As far as they could tell, it had originated as some type of skin cancer, but they were never able to find it. Dad is convinced that JPII intervened, as a favor of one old-time Polish Scout to another.
I'm sure this story would have certain types of American Protestant Christians up in spades about Satan and the lies of Catholicism and any number of things. Dad probably never prayed to God "in person" for Mom's recovery at all...yet she recovered. Was it JPII's doing? Sheer luck? God listening in and deciding to grant the favor despite commandments about having no other gods before him? The Catholics' reliance on saintly intervention definitely borders on that sometimes. It's one of the biggest beefs that many other denominations have with them. Yet I suppose Catholics' prayers to saints produce exactly the same proportion of results as Baptists' pleas to God, or atheists' really hoping that things go well. And getting the right medical attention improves the chances of a positive outcome in every one of those situations as well.