OSHA's 1910.1200 Hazard Communication Standard gives the employee the right to know the hazards and safeguards of the chemicals in the workplace to which he/she is exposed. Employers are responsible for maintaining and providing such information.

If the employer your mechanic is servicing does not provide the chemical information, it is your company's responsibility to obtain the information for your employee. In your scenario, both of the employers could be cited by OSHA for failure to provide the hazard communication information.

For the safety of your employee and the liability imposed on your company, I would tell that employer to find another service provider if the employer you are servicing will not cooperate and provide the information.

Google: OSHA 1910.1200 Hazard Communication