I agree that a school has a perfect right to *watch* students' public behavior outside of school, such as posting blogs. The difficulty arises only if they want to impose a punishment for something done outside of the school and not directly affecting it. This in turn depends partly on to what extent the school can be trusted to administer justice fairly.
Frequently, public schools make the headlines for imposing a totally unreasonable penalty on a student; it's as if they don't know how to back down after making a mistake. I'm afraid that might happen here: a school administrator completely misunderstands something on a web page and lowers the boom.