Did you apply for the job in response to a posted vacancy? If so, did it state the minimum qualifications for the job? Did it state that graduation from an accredited program was required?
Regardless, an employer can establish the requirements for its jobs, including a degree or training from an accredited program. You chose the institution from which you attained your degree. I assume that you knew it was not accredited. The employer is not required to change its requirements because of your choice or your belief that the training you received from the non-accredited institution is comparable to the training at an accredited institution.
You asked the agency to grant you an exception and it declined. I see no employment or labor law issue in your situation. You simply don't meet the agency's requirements for employment.
You indicate that you got your training in the 1980's. That's awhile ago. Maybe you should consider updating your training or acquiring a post doctorate degree at an accredited program or doing whatever is necessary for you to meet the educational requirements for this job and others that require a degree from an accredited program.
Why do you believe that the "secretary and the agency" have different educational requirements for the position you sought? If the job requires a degree from an accredited program, some secretary - years ago, if the standard was imposed in the 1980's - decided that the doctoral degree had to be earned at an accredited institution.

