He said it. There’s a great deal of evidence in support of it, as previously stated, and little against. Another piece in support of the idea is the aforementioned letter of Rav Elchonon, the Chofetz Chaim’s talmid muvhik who the CC recommended as his successor.
Sorry, but a letter purportedly 87 years old that suddenly appears 29 years ago in zionist literature doesn’t support its veracity. Where was it for the missing 60 or so years? Especially considering the forgeries that have been introduced. And the story about the Knessia you quoted differs from the previous versions proffered here.
Regarding the fake KK, I’ll suggest again procuring a copy of Mikatowitz ad Hei B’Iyar. Your answers are there. I don’t have the timeline in front of me, but as I recall R. Kasher printed the KK years later, after many of the alleged signatories had already passed away. And it did not garner the widespread attention you seem to assume it stirred. About the internet: you are speaking of communities that have largely shunned the internet. By far the internet is loaded with those taking positions against them that generally go unresponded (not only on this issue.)