SeaBass, all that needs to be said in regards to this thread, has been said. May the Holy Spirit give you revelation. Your hypothetical with Joe fails in one account. You assume it means he denied his faith (in Jesus Christ). Let me share what I saw on a site.
From site: Notice that Paul said that those who don't provide for their own have denied the faith, not their faith. This makes a distinction between denying the doctrines of godly conduct, and individuals renouncing their personal faith in the Lord
So, in regards to what that site said, I will add upon that and show you a verse that represents the truth of whats being said (that is, the faith(doctrine/conduct) and not their faith[in Christ] of salvation).
2 Corinthians 13:5-7
New King James Version (NKJV)
5 Examine yourselves as to whether you are in the faith. Test yourselves. Do you not know yourselves, that Jesus Christ is in you?—unless indeed you are disqualified. 6 But I trust that you will know that we are not disqualified
7 Now pray to God that you do no evil[emphasis added, conduct], not that we should appear approved, but that you should do what is honorable, though we may seem disqualified.
See, Paul is basically pointing them to Christ, and to their identity. Ever hear of "We are the righteousness of God, in Jesus Christ"? He is calling them to who they are. They aren't disqualified, but realize who you are. Realize who is in you, Jesus Christ. As some preachers deem it "Right believing leads to right living." He isn't condemning them, he is reminding them of who they are, that Christ is in them.
So again, is such a man saved? Is Joe saved? He '"may seem disqualified" but as Paul says, "But I trust you will know that we are not disqualified." However, sure enough, his conduct will have chastisement, for the betterment of himself and for his family. We aren't saying his conduct isn't "evil", yes he should do what is "honorable." However, he is not disqualified, for his quality is not in himself but in Christ. Joe is the "righteousness of God, in Jesus Christ."