Except I don't see this as such a situation. For one thing, it's very quick - in and out, no personal discussion about oneself. There was no disrobing involved. Everyone's clothes stayed on, and - more importantly - my daughter would have known that her clothes were supposed to stay on because I would have told her before hand what to expect. I totally trust my daughter to speak up if she feels that she's being handled in the wrong way. Also, there were many other adults and children around, just outside the door.
The room sounds very cramped - if mom hadn't been in there taking up space, would the doctor have been able to maneuver into a better position to feel the child's spine?
Me, I would have asked my kid if she wanted me in there with her. And then I would have gone with whatever she says.
And all that is okay for you and what you are comfortable with, but some parents would do things differently. I personally would not be comfortable. And yes this could become that situation, quite easily and it doesn't require anyone to be undressed and not ever child would handle it like yours. A young girl or boy can still be put in a very vulnerable spot by a doctor when they are alone in a room, and it can happen in a matter of minutes.