The only evidence I see up thread is your assertion “Twitter also explicitly exempts information available from public sources“ which is a stronger statement than Twitter’s own privacy page (“If the reported information was shared somewhere else before it was shared on Twitter [...] we may not treat this information as private”.) Twitter uses multiple factors to determine if a post is a violation, not all of which have to be satisfied, and of which being available through other sources is only one. Twitter also has a history of taking action against users who share otherwise publicly available information if the intent is malicious.

While it’s a debatable point, it’s most certainly not “plainly false” that he violated the TOS; Twitter would be well within bounds to take action against his account.