No, you did not refuse to engage, as there was no debate, but you refused to answer the questions.
That is essentially admitting defeat, not refusing to engage.
Answering questions is not *engaging*. It's simply answering questions.
Now, wait, was a subpoena issued? Is someone here the prosecuting attorney?
You may demand to have a discussion, but others may find you so unpleasant that they disagree. Anything is possible. Anyway, refusing to answer someone's set up question is refusing to play a game wherein the other guy makes all the rules. Playing such a game would be ridiculous.