In this case the government isn't just
allowing the school to use judicial procedures the government itself couldn't use without violating due process, it's
requiring them to. That's different.
And movie distributors and Boy Scouts are not the government. And when a private organization deals unfairly with a private person, due process is still available in the form of a court proceeding (e.g. a suit for unfair termination), but in this case that would either be dismissed (e.g. because the school was following federal requirements) or put the school in an impossible situation where the federal requirements require them to use an unreasonable procedure that subjects them to legal liability by an innocent accused person.