Short answer. You are still paid. Article 174 says that where a third party is legally liable, the injured employee or the dependents are paid by the System anyway. But once benefits are paid the System is subrogated to your rights against that driver, so the claim against him is no longer yours alone.
What the law says
When the disability or death is caused by circumstances creating a legal liability against a third party, the disabled employee or the dependents, in case of his death, shall be paid by the System under this Title.
Labor Code, Article 174 — Third-Party Liability And Subrogation. Read the full provision →
What the law says
the System shall be subrogated to the rights of the disabled employee or the dependents, in case of his death, in accordance with the general law
Labor Code, Article 174 — Third-Party Liability And Subrogation. Read the full provision →
Someone else's fault does not delay your benefits
The first thing the article settles is that you are not left waiting while blame is argued about. When the disability or death is caused by circumstances creating a legal liability against a third party, the disabled employee or the dependents, in case of his death, shall be paid by the System under this Title. The existence of a driver who can be sued is not a reason to refuse or suspend compensation. That matters most in the weeks after an accident, when income has stopped and a civil case against a stranger is a distant prospect.
What subrogation means for your own case
The second sentence is the trade-off. Once benefits are paid, the System shall be subrogated to the rights of the disabled employee or the dependents, in case of his death, in accordance with the general law. Subrogation means the System steps into your position as against the driver, to the extent of what it paid you. You are not collecting twice for the same loss. So the question is not simply whether you may sue, but what part of the claim against the driver still belongs to you and what part has passed to the System.
Anything recovered above what was paid comes to you
The article does not let the System profit from your injury. Where it recovers from the third party damages in excess of what was paid or allowed under this Title, that excess is delivered to the disabled employee or the other persons entitled to it, after deducting the cost of the proceedings and the System's expenses. So a recovery larger than your benefits is not absorbed; the balance is yours. That is worth knowing before you agree to any private settlement with the driver or his insurer.
What to do while the facts are still fresh
Two tracks are now running, and they interact. Report the accident to your employer and get the incident recorded as having happened on duty, since that is the foundation of the compensation claim. Separately, secure the police report, the plate and the driver's details, the identity of the company operating the vehicle, medical records and receipts, and photographs. Take advice before signing any release the driver's insurer offers, because a settlement made without regard to the System's subrogated rights can cause difficulties later.