Technique is the key here. If she is using oil expect she is adding the eggs before the oil is hot, she is probably also rushing her attempt to turn/flip/scramble/move them. One of the hardest things to learn when frying eggs is to walk away immediately after adding the eggs to the hot pan.
I notice you are in Germany, I don't know what your access to the USA's "Food Network" is but this episode of a Alton Brown's "Good Eats" can show your wife "eggsellent" technique.
(pardon the pun, couldn't resist...)
New Links:
Good Eats: https://www.youtube.com/watch?v=Fx8up7UJv2s
Alton Brown on CBS Morning Show: https://www.youtube.com/watch?v=pD3QeyK4bJY
There are two parts to this question, the stated part, and the unstated "are you really frying an egg if there is no oil?"
For the first part, most manufacturers of non-stick pans claim that their product makes oil unnecessary, and generally I've found that to be true. A little oil helps, but "necessary" might be a stretch.
To maximize your non-stickyness of a non-stick pan, you should always preheat the pan before adding the food, at least to 250F or so. Preheating causes the teflon to expand a bit, closing up pores and micro-scratches in the surface.
It is also common for oils from the past to form a polymerized layer on top of the teflon, making the pan more sticky. This is actually worse when you use aerosol spray oils, because the tiny droplets hit the pan and very quickly polymerize to form a slightly sticky layer. This layer is similar to the one you intentionally create when seasoning a cast iron pan, but in this case it is not helpful. All-Clad recommends periodically cleaning teflon pans with a light scrub of baking soda and water to remove that coating of oil. It should bring back the maximum slippery of your teflon.
When cooking protein-rich foods, you can also minimize sticking by letting the food cook a bit before attempting to move it. The loose, floppy denatured proteins in an egg are extremely sticky, but when they coagulate (set) from cooking, they become less sticky. It may seem impossibly sticky at first, but may release on it's own after a minute of cooking.
As to the second, unstated part, oil provides flavor, and is also a heat-transfer vehicle. When the food is on the pan, if you looked at it with a microscope only a small portion of the food is actually in contact with the pan. Those areas will get heated more, and other areas will get heated less. A little oil fills those gaps, causing more even thermal contact, which allows fried food to fry, rather than just get burned in some areas.
It is really a matter of taste whether the flavor of the oil and the way that it changes the texture of the food is appealing to your boyfriend. I wouldn't like it without any oil, but if he does, well, so be it. If he doesn't really like the taste, but is concerned about health, I'd suggest using a little olive oil - it has no cholesterol, is low in saturated fats, and has a good flavor. Different than butter, but still very enjoyable.
Best Answer
Adding oil or butter makes scrambled eggs more creamy by giving the egg protein something to hold onto and not curl as tight.
I didn't like scrambled eggs until I tried this formula and it's awesome.
Credit goes to either Jack Bishop (Cooks Illustrated) and/or Nathan Myhrvold (Modernist Cuisine) unfortunately I can't remember which of the two clever gents I heard it from.