PBA: Ah, that makes sense. It’s a D’rabannan so it’s S’feiko L’kula. My Chiluk doesn’t work for you though? We don’t know which is Assur so we treat each individual case as Assur. But at the end of the day it might have come from a Muttar spot. So if you don’t know what that spot is then as long as you have a way of Bittul you can use the Bittul.
(The single egg with a blood sport itself is a Safek D’oraisa. And even if it was D’rabannan this would be analogous to the case of the 4 Kosos; see the Ran there in the last Perek of Pesachim.)