For this, I was referring to Oden's flashback. Higurashi referred to Yamata-No-Orochi as giving Orochi the power to be Shogun, but it was never followed up on:
So my speculation is that this fruit is in the same class as Okuchi-No-Makami.
So my speculation is that this fruit is in the same class as Okuchi-No-Makami.
This also bothers me, because if he wants people to think Yamato is joining, he's not doing a very good job. The non-Japanese community is already pretty split on the chances, but the Japanese community matters much more, and the general consensus there is that Yamato won't join. It was mixed before the last few chapters, but the guardian role hits close to home for Japanese people. The Inu-Inu fruit also violates the 2929 rule, which most people took to be a flag that Yamato can't be a Strawhat.
All the reasons to suggest she won't join come from subtext, looking at relationships and general understanding of context and Oda's storytelling. Whilst the biggest reasons to suggest she will join are the surface level statements where she plainly states that she expects to sail with Luffy. A lot of people genuinely think like "Yamao said she will sail with Luffy...Therefore Yamao will sail with Luffy." Completely disregarding the fact that they're reading a story and it's a part of the author's job to deceive and mislead you to keep the story fresh and interesting.
Stuff like the number theory, knowing the ending of the myth of the Makami, analysing "nakama criteria"... These are all things the average reader just doesn't know or do. Those are the people Oda's generally writing to mislead since not everyone is going to fall for a red herring.