This myth is likely to come from a Christian, particularly a Protestant. The idea that all human beings are depraved sinners who know that they are depraved sinners, unworthy of forgiveness or eternal life, has long been an important aspect of Christian doctrine. God, however, is loving and generous enough to forgive us despite how horrible we are. If a Protestant Christian sees this as central to their own life, they may assume that it's central to others' lives as well.
Read Article: Myth: Atheists Fear they are Too Sinful to be Accepted by God, Fear Judgment