Doctors billing primary & secondary ins company for same amount?

Yes. I work in a medical office and can tell you that your Dr. is correct in the primary ins. should pay its part and only what is not paid by primary is supposed to be paid by secondary. Many big companies do whatever they think they can get away with- call your ins. companies and inform them of what is happening. They will make short work of it and will appreciate you notifying them of the problem.