I do fly EK quite a bit and find that even getting to the airport early does not guarantee you an exit row seat.
Observing the pax who seem to be able to snag an exit row seat, there are many people from Eastern Europe as well as the Middle East, including many slightly built females.
So I just put it down to corruption at many airports in those regions and shrug my shoulders.
Just another poor business practice of EK, and it is very annoying.