I think the problem is probably one of insurance (both liability and company personal insurance). If training has been completed but not in actual pocession of your initial licence the legal eagles may argue that by not holding the correct documentation you were not adhereing to the regulations laid down. Should you have an accident, were you or an aircraft/pax etc was damaged/injured the company may find their insurance cover invalid. They could potentially expose themselves a claim they could not cover.
Cheers Bondy