Judgment-proof in the sense that the operator has no assets with which to pay the judgment.
The operator here is liable. But if the operator has insufficient assets to satisfy the damages, the owner is a more sensible person to bear the costs of the accident than the injured party.
When a joint enterprise accidentally injures a third party, generally all possible outcomes are fundamentally unjust. That's what makes tort law interesting.
It appears you're suggesting a structure of a business, where the owner isn't leasing to an unrelated party. An employer is liable for the actions of his employees (even non-employee employees) through entirely separate and much more appropriate channels.
The operator here is liable. But if the operator has insufficient assets to satisfy the damages, the owner is a more sensible person to bear the costs of the accident than the injured party.