I am 100% sure that is incorrect. Last week, my Evoker friend had Heroic Kharnalex in the first slot of his vault and he had only killed the first four bosses on Heroic. There are also many screenshots on Reddit of people getting Great Vault options from bosses they either haven’t killed at all, or haven’t killed on that difficulty.
That being said, I vaguely remember someone from Blizzard saying any loot is possible, but it’s less likely if you haven’t killed that boss. I don’t know if that was specifically a SL thing or a permanent thing though.