The title is asistant researcher. Half of the duties are administrative. The job posting said bachelor preferred.
From what you said, as long as the company can justify that the job needs a bachelor degree, it would be fine. I inferred.
-Correct, but your professional training/skills has to meet this job requirement and the salary has to meet the prevail wage level. You had better hire a lawyer and your lawyer know how to deal with it. At least you need to consult a immigration lawyer for this issue because a PH.D. holder for secretary job is not normal.