His lie was saying that stomping on a symbol has no meaning. Of course it has meaning. So, that would be a lie. Maybe so blatant it was intentional, in which case, as I said before, he has taught a valuable lesson on why not to lie, or perhaps more scholastically, that shock use of irony/sarcasm is a poor tool for use in teaching. If it was not a lie, then he doesn't understand how symbols work.
From the OP:
"This is a symbol of America. It is just cloth. This doesn't mean anything,"
Of course the contradiction in his sentences was intentional and introduced cognitive dissonance, provoking thought.
IMO, a highly effective teaching mechanism.
Except for the students who were too outraged to think about the contradiction.