Yeah, that's totally wrong. It's just math. Negative whatever hp plus whatever positive energy is healed equals hp after the channel. Entirely possible to heal someone and have them stay unconscious (but crucially stable and no longer bleeding out).
If any sort of healing cures the dying character of even 1 point of damage, he becomes stable and stops losing hit points.
Healing that raises the dying character's hit points to 0 makes him conscious and disabled. Healing that raises his hit points to 1 or more makes him fully functional again, just as if he'd never been reduced to 0 or lower.
Ummm...experienced or not, he is incorrect. Your mage could have taken the 8 healing (taking him to zero) and then used his action to drink a potion for example, to get himself to positive HPs.
Sounds like he's thinking of 4th Edition.