The location was irelevant. To give you a chance to understand, Syansu, I repeat: THE LOCATION IS IRRELEVANT!
It is against the law in the US to take public education funds and then teach a religious doctrine. That is what the woman was doing and she was violating the law, not to mention common sense, good taste, and the principals of science.
She can believe and advocate whatever she wants in her home What she cannot do is take public educational funds and teach religion. ID is religion, as has been found both by the scientific community and several different judicial jurisdictions.