I appreciate the argument. It's a good one. (I actually wondered when someone would articulate it as you have.)
I think the confusion comes from Christians not remembering that in the gospel 'believing' implies 'trusting', not just being aware and agreeing that something is true. We are saved, not because we know and agree that something is true, but because we have put our trust in what God has shown us to be true.
That's why I make the distinction between 'faith'--simply knowing that the gospel really is true--and 'believing'--actually putting your trust in what God has shown you to be true.
See, every unbeliever whom God has called knows the gospel really is true, because the Holy Spirit has testified to them that it really is true. But they reject the faith that God is providing them to believe and trust in the gospel and be saved.
"6 ...it is the Spirit who testifies, because the Spirit is the truth.
9 ...God’s testimony is greater because it is the testimony of God, which he has given about his Son.
10 Whoever believes in the Son of God accepts this testimony. Whoever does not believe God has made him out to be a liar, because they have not believed the testimony God has given about his Son." - 1 John 5:6,9,10
See? The BELIEVER is the one who ACCEPTS the truthful testimony of the Spirit. While the unbeliever rejects it. It's not that the unbeliever does not know the Spirit is speaking the truth and, therefore, can't trust in what is shown him, but rather he has chosen to not believe what the Spirit of truth has shown him to be true.