Freedom of speech does not mean you can say anything anytime. Freedom comes with responsibility and accountability. If you don't behave accordingly, yes, you're fired.
The lawmaker's backlash was primarily because of the reference to Hitler. It was a rhetorical reference, but not exclusively. It was also an appeal to those who have an endearment for him, an appeal to the worst in humankind. She was speaking to a crowd that perhaps hear those words as affirmation to their own biases.
What was the lawmaker's intent? I question it. Not for a minute was it solely the "underlying principle of the thing." Instead, I suggest we examine the underlying intent, a less appropriate one, camouflaged be some perhaps good principle.
I reject the premise. The lawmaker, and you to a degree you, seem to suggest that the government has a scheme involving education. When Hitler spoke those words, he had the Hitler Youth Movement in mind. Indeed, indoctrination and brainwashing was the purpose. The lawmaker, by bringing up Hitler, seems to compare U.S. education with that. Additionally, the lawmaker is speaking to a crowd inferring and interjecting that, in my opinion, false premise, as a matter of fact.
On the contrary. The United States education system is based on a word that is primarily used only in educational circles called "pedagogy." I can speak from internal and external experience. Teachers are trained to teach using five basic pedagogical (methods of teaching/learning) approaches... Constructivist, Collaborative, Integrative, Inquiry and Reflective. It is the opposite of brainwashing. Instead, the methods promote independent thinking.