Aiwendil, I have stated that this was a "belief" that men had. It does not have to be true for it to be a belief.Okay, I agree with this. "Belief" in this sense means an approximation, not actually taken to be the truth. My only hesitancy was that you equated this with "faith", a word often used in quite another sense: belief that a thing is the single and absolute truth.
As you know already, this "belief" would contradict with the conception of the Ainulindalë, that Men already had their gifts before the creation of the world.
Yet, in all beliefs, there is a "flicker" of truth, and in this case I believe that there was a "diminishment" of the life span of men; I'm not saying that they were immortal, but just that their lifespan was greater.