I haven't seen those rules yet but that's how it worked out recently:

The STPC matter was quite a challenge on my trip CAI-DXB-SYD. CAI office told me that they are the only ones to issue it as they issued the ticket. I called EK reservations in Germany several times to arrange for pickup in FRA on the day of my flight STR-FRA-CAI connecting to EK DXB-SYD. Spoke with different agents getting different answers : After several unsuccessful calls one FRA call center agent finally offered me to prepare the voucher in my booking/PNR for pickup in FRA. When I connected in FRA I went landside to the EK check-in/ticket desk in T1/C. Too bad the desk was due to open at 10:00 am and my flight to CAI was about to leave at 10:15 am . I called EK reservations immediately and another agent told me again to pick it up in CAI (she told me that I cannot collect it on arrival in DXB or in FRA anyway) and wished me luck. The EK agent in CAI handling the transit procedure in that infamous "long waiting transit area" delivered the voucher to me at the EAS lounge after requesting it on my initial contact with him in transit. A little bit of a hassle but it worked well in the end.

Send EK CAI an email incl. your passport number/issuing country and follow my procedure in CAI - this should work well.