Thinking about it, I think that it is true that the fruit didn't directly give the Rinnegan to Hagaromo. Especially due to that scan and your reasoning with Kayuga lack of Rinnegan compared to Hagaromo. But by the same token, there isn't a connection between being the Juubi Jin and gaining the Rinnegan because of it; Obito had no effect whatsoever, despite using a lower Juubi. The full Juubi may give the Rinnegan, but the evidence is inconclusive at this point.
The single and thus biggest piece of evidence that we have is this:
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Which points to the strong possibility that Hagaromo may have almost died while fighting the Juubi, and then awakened the Rinnegan. He may have gained the necessary Yin/Yang prerequisites from the fruit and all that is needed is the verge of death condition.
How deep does this verge of death condition need satisfied? Probably pretty darn close. Madara said that the instant before gaining the Rinnegan was his verge of death. But why would he be saying that when he was already alive, despite being very old, and not in immediate danger? I think this is the sequence of events: Madara is about to die of old age ----> Madara gaining the Rinnegan----> Madara summoning the gedo---->saving himself the split second before he would have succumb to old age.