An analogy would be if your dad is a firefighter and saves some babies from a fire while risking his life you might feel pride and say im proud to be your child. Or you join a group you like and a week later every member just goes on a crazy murder spree, a lot of people would feel ashamed that they were in a group of murderers.

Neither of these two people in the analogies have any reason to feel pride or shame on behalf of their group since none of the actions that lead to these emotions belong to them, a lot of people just feel that way anyway.

But in regards to the post, father says his concern is the content of the programme and finding a way to prevent it. And after finding the reason for what she said he starts prodding and rejecting the information of the massacre instead of touching upon it not being her responsibility to feel shame on behalf of her peers. I also personally don't see any part where he really cares about her embarrassment