Serious Eats - seriouseats.com

If you watch Julia Child doing a French omlette, she adds a bit of water and uses an extremely hot pan. The omlette cooks is maybe 20-30 seconds with constant shaking. The methods that add milk or cream are low heat methods, and cook much slower. Both are good, just depends on what you like.

I find adding a splash [ only a tsp or so per egg ] of water helps to breakup the protien molecule that easily join up into chains [those stubborn glops of white] while whisking to achieve a homogeneious blending of white and yolk quickly .Its a bio-chem thing where the ends of protien molecules like to attach to another molecule thats why eggs will blend and bind so well with other ingredients and water is an excellent neutral liquid to serve this purpose . It may be a tad thinner but thats only from the protien molecule chains being broken down to a smaller size and may even add to the fluffiness . I dont get watery scrambled eggs by not over cooking them .
If I have heavy cream on hand I use it instead if I want a little richer result , say for a fried egg and cheese sandwich , but by whisking thouroughly they will still be fluffy but maybe not quite as much. As mentioned when adding dairy you must watchout for burning.
As fast as eggs cook [even on a medium heat] I wouldnt turn away from them especially towards the end.
I'm going to make myself an egg and cheese sandwich now for my "BRUNCH". need a quick bite to get me through til supper at 4 P.M.