Yeah, you're right. Specifically using the claim made. You can read about it in the NTS wikipedia I linked above.

Since Alpharius provided no specification for why he is not a ninja, and only mentioned "extraordinary claims" as a point against him, I think it is sufficiently close to at least reference it.

Here's an example. "No true ninja would make extraordinary claims. Bujinkan guy makes extraordinary claims, therefore he is not a ninja."

The particular reason this is interesting, though, is that the extraordinary claims in question are his claims to a legitimate ninja lineage. If this counts as an extraordinary claim, then in fact, ALL ninjas are not ninjas, because there is no ninja lineage I am aware of that is not in contention.

My argument is that it is not a lineage that makes someone a ninja. It is a consensus. If enough people agree that someone is a ninja, then they are a ninja. That's just how language works. Bujinkan dude is definitely covered by this definition of ninja.