This is what the OP questions though, in regards to believing one CAN be healed. I am sure many believe God can heal them, they read of all the miracles in the Bible. Yes, He can, but is He willing? Even more importantly, and getting to the heart of the matter, is He willing for you?
I can believe that the glass of water on the table in front of me can quench my thirst, but it won't if I don't step out and drink it (in faith). You see, acknowledging the capability of something is not the same as utilizing it. In the same way acknowledging God's ability to heal the sick is not the same as believing in faith to be healed.
One simply believes He can heal the sick, the other believes He will heal them. One is ripe with expectation, the other with a hope. One obtains it, the other dreams of it... and of course, there are those whose hope is fulfilled and God steps in, in His mercy and grace though they held no faith.
There is a distinction.