You're pulling the same thing her campaign management did - total damage control. By taking an over-literal stance on her response you're downplaying the obvious. Of course it doesn't say word-for-word "separation of church and state" but we all know that's not what she meant. The first amendment prohibits making any law respecting an establishment of religion, including the state level.
What really gets to me though is how these creationists try to pass their archaic doctrines as science. They were beaten in the courts, Kiltzmiller vs Dover School District, and that should be the end of it. So what do they do? They try to change the constitution. Coons is right. If you want a religious education go to church or go to private school. This garbage has no place in our public education system.
Here's a great documentary covering the Kiltzmiller vs Dover trial: