There is nothing that I can see in the Corinthian letters that makes me believe that Paul thought he was dealing with non-believers. Had that been the case, he would not have referenced the amount of time and prayer he had put into them when he had been with them. He was chastising them because they were believers, not because they were unsaved. We cannot chastise people who are not Christians, as if they are Christians.
Dr. Fred has written numerous books and articles that cover a wide-range of theological topics and he endeavors to present the study of God's Word in a clear fashion, helping the average layperson comprehend the great truths of Scripture.