I wouldn't worry about it, keep on doing what you're doing momma! You'll start to see when they desire privacy, so maybe just try be conscious about that, but I wouldn't change anything you are doing.

I thought it was a little weird how the doc responded, but after reading another comment about the default privacy position, I kind of get it.

But I do want to say that as my children grew older (6-10ish range) and we went to appointments, their doctor certainly did ask them (or me) if they wanted privacy (I always had both of them with me, girl and boy, 16 months apart in age). I did appreciate that, as I wasn't sure what was the 'right' thing to do, either!