I think it might be otherwise. But this is of only me interpretation: The gift of men from the beginning was to leave Ea and time when they were tired of it. None of the unfallen men had reached that stage before they were corrupted. So they were in their own view immortal. They never had the idea that the parting of soul and flesh was a part of their nature. When they rebelled against Eru he punished them with a short live and a death that came unwonted. And since never before had any of them died they thought death it self was their punishment. But that was not true and might have be a lie of Morgoth. (Don't forget that even the fathers of the three houses came from fallen men that repented.)
In regard to this special question, we have also to think about the time line. The Athrabeth is a round world story and the fall of men had in that version already occurred when Morgoth was in Valinor to teach the Elves about men.
Respectfully
Findegil
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