I know lawyers who dealt with this, and I know people who went to jail over this.
How do you know whether an organization is "dedicated to the violent overthrow of the US government?"
Government agencies used to give a list of organizations, and ask whether people were on it. Otherwise, the question is too subjective to establish whether somebody is "lying."
How do you define "belonged"?
Pete Seeger supported the Communist Party, but he never joined it. He could honestly say that he never "belonged."
Just because she baked cookies for the Committee Against Genocide and the New Movement in Solidarity with Puerto Rican Independence, that doesn't mean she "belonged." In fact nothing in the article says she "belonged" to the organization. So you ought to re-read the article.
In fact, nobody knows what the questions were, because the agent didn't record it, and destroyed his notes afterwards.
Given that agent's hostility towards "liberal college professors," it's reasonable that he distorted her answers. There were many cases, especially during the McCarthy days, when a government witness would claim somebody had said something, and memos in the government's files would show that he never said it. Why do you think they don't record their interviews, the way Verizon customer service does?