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I believe your second "theory" would be the correct one. I don't think there is anything to make us question Otoha's existence, short of assuming Takuma "imagined" her as well ... but i think that is making things more complicated than they need to be, and Takuma imagining a spirit that matches the one from story Hotaru wrote while being unaware of it is stretching things a bit thin.
Otoha was there before Takuma started imagining he could see as well, (and in the end he had already come to terms with the situation for a few years already, so there was little reason for him to suddenly see a hallucination. If he had indeed remained in his delusional state it would be different, but that was long since gone). So ... at least in my opinion, there is nothing to imply that Otoha (Hinata) wouldn't be what she was always shown to be - a supernatural element of the show.
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