This is not a policy of "one Leshan, one Sichuan", but a policy of national unity. As long as you have obtained a military driver's license during your service, you can apply for a new driver's license of the corresponding level after retirement. If you didn't get a driver's license when you were in the army, you won't get any preferential treatment from veterans. You will get a driver's license through study and road test like everyone else.
Because the driving schools all over the country are commercialized now, the relevant laws and regulations of the army have no preferential treatment for retired soldiers to get a driver's license for free. Only retired soldiers with resettlement conditions can freely choose their jobs and receive corresponding fees, so paying driving school fees is free in a sense!