Nope, they did not have Rock solid Faith to begin with, most Christians that claim to have faith for healing end up experiencing what I call Faith failures, I call them unbelieving believers because they've never taken the time to develop faith in different areas of their lives especially when it comes to healing and provision, this is everywhere in the Bible especially the New Testament, my mother who just went home to be with the Lord at the age of 96 was in healing verses for many years overcoming many many things that many of her friends never did because they never did what she did, and just the fact that you mentioned that they were begging God to do something for them is proof that they had no faith or little faith or what is called underdeveloped faith, the faith that God uses it's called fully persuaded kind of faith found in Romans 4:21, in Mark 11:23 Jesus himself said you must not doubt at all but believe so we need to realize that we have doubt in our heart and get rid of the doubt or wavering, shalom