If this is true, then Privacy.com doesn't resolve this obligation. The temporary card number won't be chargeable by the merchant, but you'd still be on the hook for the renewed (and unpaid) service.
It certainly changes the burden of notification. A company can setup many hoops for canceling, forcing you to go through some asinine phone tree and drone script to stop charges to your card. Whereas lacking an established payment channel, they can no longer play dumb if you eg send them a simple email to cancel.