You can just use water, like Aunt Bea described and as blissful does - she doesn't cook with any fat at all. What you call picky I call precise. Steaming and frying are not the same things.
So I did that this morning. Added less than a Tablespoon of water to the pan, cracked in 2 eggs, popped a lid on. Didn't check time, but by the time the toast came up they were done.
Have to be careful in the amount of water as when taking the eggs out it could be easy to get water on your toast = blech.
So depending on the pan I use I may still use a fat of some sort and fry for a bit - then add water and a lid to finish with steaming. So there you have a Steamed Fried Egg.
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