It is irrelevant whether God actually causes people to become sick or not. If God personally makes a person sick, or, if He allows Satan to make the person sick amounts to the same thing. God is in control of all things, as the Master Creator of all things, He decides what goes. Nothing happens without His say so...So, if sickness happens that He didn't cause, it exists because He allows it to exist. Therefore, the argument that God wants everyone to be healthy and well is void, because if sickness exists, He allows it. If poor people exist, He allows it. If evil exists, He allows it.
Doesn't mean He likes it, but if it exists in this world, it exists because He allows it. He could solve it all (and will) when He wants. Currently, He doesn't want everyone to be perfectly healthy and to live forever. If He did, we would.
God allows 'bad' things to happen for a myriad of reasons. One of the biggest seems to be as an attention-getter. If I am perfectly healthy, prosperous, rich, powerful, well-liked, etc...why would I need God? God knows that we sometimes need to see what the gutter feels like before we know to reach up to Him.