I believe Paul was pointing out that Eve was deceived by Satan initially, not Adam. He didn't go into depth, leaving it open for interpretation. You have your opinion, I have mine, so we can agree to disagree. I don't believe Paul was giving more information on what happened in the Garden.
Genesis 3:6 "Consequently, the woman saw that the tree was good for food and that it was something desirable to the eyes, yes, the tree was pleasing to look at. So she began taking of its fruit and eating it. Afterward, she also gave some to her husband when he was with her, and he began eating it."
Genesis 3:17 "And to Adam he said: “Because you listened to your wife’s voice..."
If you can show me where it says Adam knew he was going to die, I'll change my opinion. He knew he was disobeying Jehovah, but he "listened to his wife," who had been deceived by Satan. Therefore Adam could have believed the lie she was told by Satan.