Try Maybe they didn't like what I said. "Mind" in the sense of "dislike" is used in the negative and in questions. For example, I was afraid I had insulted him, but he said he didn't mind. (He said he did not dislike my statement.)
Do you think we can generalize to say that to mind in the sense of "dislike" is used in the negative, in questions, and in responses to (real, rhetorical or unstated) questions?