Militant atheists share the same logical flaws as radical Marxists.
Lack of self-reflection.
Pretty sure the statement was just proved as either inconsistent if it excludes itself from its own pronouncements about statements advanced without evidence, or, if it is consistent then it must abide by its own logical requirements about statements advanced without evidence, of which it is itself such a statement, and therefore ca be dismissed without evidence.
Subjecting a statement to its own logical standards for all statements is not 'twisting' it, it is testing it for internal consistency.
It's not a perfectly good statement, it's either inconsistent or it can be dismissed without evidence by its own account.