Even if common place and industry/FAA practice, it is still just wrong. A rating exam, Type exam, line check, proving run, Even an A&P exam is another deal. I have allowed the FAA to sit in on exams several times myself. During a training scenario, as the OP describes, it seems completely uncalled for and very unprofessional on the part of the inspector. The mere presence of the inspector could be an impediment to training and possibly even prevent the student from asking certain questions. This is a bad deal. Even then, the Inspector is too observe, not ask questions or otherwise interject or distract. There is no reason for this inspector to be continually/chronically engaged in conversation which is distracting and contributes nothing to the educational experience. In fact it is contributing negatively to the students experience. This is expensive training which the student is paying for. It would be fine with me, as a taxpayer, for the FAA to accomplish this goal in another manner, but not literally at the students/customers expense.