well its not so much that i doubt it as this: odin at some point started out in his most original form as a sidhe. after gaining followers and acruing power through various mean, he became
more, hence his ability to handle iron. odin still holds(or perhaps captured it somehow, when people first believed in santa?) the kringle mantle which is a fae mantle. idk if as kringle iron becomes his kryptonite though... so yes, odin was fae, he holds a fae mantle. but he himself is not beholden to the nature of being of fairy anymore. specifically you might say its because he has his own demense
but so does erlking, so thats inconclusive evidence.