So how can it be that Obama is suddenly responsible for the actions of a teacher in an elementary school? Simply put, they can't. We cannot hold Obama responsible for the actions of every teacher throughout the US. To try to do so would be insane.
That's not to say that the actions of that teacher and to some extent even the school ought not to be scrutinized. No, indeed they should. However, we should be sure to see the whole picture before we go too deeply.
Now this doesn't mean that we should not criticize him. No, we must. We must find fault with his actions and his decisions whenever we can. However, trying to hold him to task because of this song is childish. In short, it just isn't logical.
I agree with these two parts of your post. If it was only one silly song from the teacher at that school then no problem, discipline the teacher and move on.
It is not one teacher in one school.