Visitor: Any person can be saved, if they will.
Response: Don't we all believe any person can come if they will? The problem is, are there any persons naturally willing to submit to the terms of the gospel? Does it come naturally for fallen sinners to come to the humbling realization that they have no righteousness of their own and so flee to Christ alone as their only hope? Can a person say "Jesus is Lord" apart from the Holy Spirit"? (1 Cor 12:3) The scripture reveals that men are so bent on wickedness (John 3:19, Rom 8:7) that unless the Spirit disarm the hostility of their hearts, turning their heart of stone to a heart of flesh, they would never believe.
Jesus declared, "the Spirit quickens, the flesh counts for nothing ... that is why I told you that no one can come to me unless the Father who sent me grants it (John 6:63, 65)
Augustine said, "to will is of nature, but to will aright is of grace."
Like you I believe the gospel must be preached indiscrimanately to all men. We are to get the gospel to men's ears, but only God can get it to their hearts.