The agency's statement says that PII is secure but that the complaint included internal emails and documents with info about the agency's systems and employees. That's not contradictory.
I suspect the whistleblower is correct, but I don't think it's proven to the point where we can confidently state that "it happened." SSA isn't trying to dispute the method, they're trying to dispute the fundamental claim.
It might be worth waiting for the outcome of the investigation before trying to dispute anything in public statements.