It's all a matter of your former employer's contract with the vendor. In this case National. Some companies include retirees. Others have a separate (lesser discount). Others don't at all.

The issue isn't whether you are asked for ID, it's whether the rate affects insurance in any way if you are not entitled to it, have signed a contract (or electronically verified) that you are entitled to the rate and are then in an accident where the vehicle is damaged or someone is injured.

You will have to do the research on eligibility.