Is that really true? Zero Data Retention (ZDR) is standard language in enterprise contracts and it seems quite egregious a vendor would want to take on that amount of liability and ignore the contract terms.
On top of that, Anthropic is SOC2 and ISO27001 so they've had _some_ independent auditing (although they could still try to hide such logging/recording anyway)
With that in mind, they also have a hell of an incentive to _not_ secretly collect that data.
Of course ZDR oftentimes comes with contract minimums so individuals and small corps are locked out and subject to the whims of the provider.