The obvious conclusion was that Jesus was exercising God's authority. Given two options, they chose the wrong one. And Simon Peter answered and said, Thou art the Christ, the Son of the living God. A. Jesus counter challenged His opponents. The real question is the actual nature of man's problem.
Sin is the root cause of all suffering.
Christianity connects iniquity and disease in the human condition. Forgiving and healing go together. Pardon of sin strikes at the root of all diseases. The challengers were more concerned about the implications of Jesus' authority than about the poor sufferer's health. I say unto thee, Arise, and take up thy bed, and go thy way into thine house.