I too have to wonder about "believe correctly". You seem to have a thought on this already.
Did not God in Samuel say man only sees the flesh "But the LORD said to Samuel, “Do not look at his appearance or at his physical stature, because I have refused him. For the LORD does not see as man sees; for man looks at the outward appearance, but the LORD looks at the heart.”
Right there.. God does not see as man sees. So if no man can see the heart.. then your question can only be answered by Him and He is not going to share. How many did Christ Himself show up in spirit telling them I am the way the truth and the life vs hearing some guy/gal on the corner or at Church or over hearing someone talk about how Christ loves them and believes.
So "who's correct" Jesus/doctrine are we running with here? I personally am under the belief most are bind and have no sin. Some say they see so their sin is still there. We do tend to judge based on only what we see and hear and feel