In the West, and especially in America, we don't highly internalize "being American" (insert country). A lot of us just think of it as a circumstances. And right now there's a lot of distaste for what the government does. You'll probably find that most of the people are upset at their own country about exactly what you're upset about what America does (I know I am, and it looks like the parent does too. At least in the specific example).
We don't always condone what the government does. We don't see that as "us" but "them". You'll see many people speaking out against the government here when they do things we don't like (that's democracy in action. The belief that governments need to be put in check). So when we don't like something we try to get it changed, and this frequently works. More often than not actually, and the nots are usually that it takes longer than we want.
So an American won't see themselves as a hypocrite for calling out a country for doing something that America does if they also disagree that America does it. We just don't see our government in that way.
Edit: The parent is also making reference to a phrase that most of our mothers taught us: "just because everyone else is doing it doesn't make it right" (or some variation)