Turtle, I don't know if EK pays less than market prices for oil (maybe in DXB/DWC, not in the rest of the world), but to answer your question consider this:
High oil prices quickly eat into the profits of an airline with high labour costs, so with the price at 50 returns a solid profit, at 75 breaks even and at 100 it's a blood bath (numbers are just an example)
For EK (lower cost structure) it's the same dynamic, only shifted to right (75/100/125)(numbers are just an example)
This explains why other lose money with high oil prices.
It takes a good shrink and a deep knowledge of the ME mentality to explain why EK underperforms today with low oil prices!!