Maybe still worth it if their "64% cheaper" figure holds.
Fine tuning you have the actual model weights of the original model, you then train that model to answer in a different (or better) way.
What you're describing is just synthetic data.
Note Anthropic misused the term in their post about Chinese model distillation, deliberately I assume.
I wonder if, similar to the American labs, they'll become stingy with their weights once they start getting immediately undercut by a wave of slightly better derived models.