It's more than just Billy Graham and John 3.16. There is also 1 Timothy 2:4 that tells us that God desires that all people be saved. And it really it is all people, not all types of people, He wants saved. 1 Timothy 4.:10, tells us that God is the Savior of all people. We know that God is not the Savior of those He doesn't want saved.
Jesus “takes away the sin of the world” (John 1:29), thus making the atonement available to all, but it will not be applied to you, me or our neighbor if we don’t look to Christ, just like Jesus illustrated at John 3:14/Numbers 21:6-9. His atonement is designed to only apply to those who believe in Him, and if you, me or our neighbor refuse God, then we will perish despite what would have saved us, just like Jesus illustrated at John 3:14/Numbers 21:6-9. No one in Hell can be told: “You had to be there. You had no Savior’s love or atonement for forgiveness, but were born helpless and hopeless due to a cruel, malicious God.” Instead, they’ll be told: “Thou fool! For God so loved the world that He gave His only begotten Son, so that whosoever believes in Him will not perish but have eternal life.”