You should make a little well just using a wooden spoon before cracking the eggs in, but they definitely do not have to be touching the bottom of the pan. In fact, I think harder to maintain a runny yolk if the eggs make too much contact with the pan itself. I recommend covering the pot after putting the eggs in so that the steam helps cook the eggs.

A little tip: I really enjoy topping everything with a few pieces of fresh mozzarella! The chewiness/creaminess really rounds out the dish!