It is definitely one of the possibilities he considered, and the one that has the most evidence in the published Sillarilium, and the one they use in the movies and the recent show.
But if the Fates don't change things for mortals, they're not altering fate. In any case, the Fates have in my estimation always been depicted as a group apart from the Olympians.
Agreed. I think I might rework Dragonborn heritage gifts to that effect, much like I did with my A5e version of draconians (each type is a different heritage gift).
Do those folks alter fate though? The Fates just know how it's going to go. Tyche and Eris don't necessarily know how its going to go, they just want it to go a certain way. And prophecy is very unreliable and open to interpretation.
Case in point: I see and understand your interpretation, but...
I can see that having some truth to it. Still, gods in most settings don't directly exert significant reality-altering influence on the mortal world much, usually due to ancient agreements between themselves, or commandments from a overgod or similar being. And fortune-telling, while commonly...