Who issued the ticket is irrelevant, it is the marketing and operating carrier that matters.
So are you saying that my upcoming flights on an Emirates-issued 176 e-ticket including 2 flights on QF metal which show up as "EK5XXX" when I look on the EK website, but which show up simply as "QFxxx" flights when I look on the QF website, will earn BA Avios and TPs for me if I put my BA number in when checking in?
EDIT: The EK PNR no longer pulls up my booking on the Emirates website. (The booking was made with a third party). Logging in to my Skywards account shows the upcoming travel, but cannot actually display any details of the flight. The flights exist as normal using the Qantas/Amadeus PNR, and show only as QF flight numbers on both the Qantas and CMT websites. I don't know whether to be worried at the apparent "failure" of the EK PNR which previously worked, or whether I should now be delighted that I can apparently just use the QF PNR and obtain BA Avios and TPs where I expected the 176 e-ticket number would make this impossible....the OTA presented them as "EK5XXX operated by QFxxx" but the only one now showing the reservation is Qantas who show no EK numbers for the flights on their metal.
2nd EDIT: I got the OTA's own PNR to show the booking on Travelport - and there the flights show as "EK5XXX operated by QFxxx". It might still be worth checking using the QF code as the first sector is actually operated by 3K...