I agree that the mother (with some input from the father) get to decide who is in the delivery room. However, I think it is rude for parents to think they get to say who can or cannot occupy the public spaces of hospital waiting rooms. The patient room belongs to the patient. The rest of the hospital does not. Provided those in the waiting room are not causing problems in the hospital, the new parents only get to dictate who sees their baby, when, and who comes into the patient room.
On the other hand, if your loved ones have chosen to have private time with their new bundle of joy, don't try to make them feel guilty for it. They will call you back when they are ready for you if they are ready for you. And the order that they call for visitors may have absolutely nothing to do with what you are thinking it means.
When DS was born, DH and I were the only ones in the room. My deceased mother's sister, Aunt S, was babysitting almost 2 yo DD. Aunt S and my father both came to town a few days before DS was born because we knew time was getting close. Immediately after the birth, I was only allowed DH and 2 visitors at a time. My dad got his feelings hurt because I called for Aunt S and DD first. He was ticked that I let Aunt S see/hold DS before the grandparents. He didn't think about the fact that in my mind I only called for Aunt S to come back because she would be bringing DD. I wanted DD to be the first person that wasn't already in the room to meet the little guy.