First of all, the waitress didn’t have a clue. Second, there are many ways to thicken a soup. Some soups – and you may find this hard to believe – thicken themselves! Most commercially produced cream soups, that is, most canned soups, and therefore, most restaurant soups are thickened with a white sauce, either a Béchamel sauce or a Velouté (a similar sauce made with stock instead of milk). In fact, most cream soups are just runny versions of either of these two sauces, with vegetables and/or other ingredients added for flavor.
Cream soups may also be thickened or finished off with a the addition of cream (heavy, thick, rich cream) or egg yolks (temper the yolks with a little of the hot soup in a separate bowl, then add them to the soup. This will keep the yolks from scrambling when they land in the soup).
When a soup is made from scratch in a restaurant kitchen, the cook is quite likely to use a hand blender, or immersion blender, to get rid of any lumps. If some of the flavoring ingredients – tomatoes, potatoes, cauliflower, etc. – are already in the soup, they will be beaten into little tiny particles, too, further thickening the soup.