Just because according to many chabadnicks think he did, doesnt mean he said he did.
This isn’t a matter of of someone claiming he said something privately. That’s the case with the denials.
This is based on public statements.
It seems like the vast majority of the intended audience, his chassidim, understood his statements as claiming he was moshiach.
Kol hakavod to those Lubavicher chassidim, such as Sechel Hayashar, who try to interpret his words differently so that they don’t need to consider him a moshiach sheker.
Unfortunately , most, it seems (although the antis claim it’s just a vocal minority) avoid considering him a moshiach sheker by either saying he’s still alive, or that he is going to be resurrected as moshiach. The problem, of course, is that this is a distortion of Yiddishkeit.