It seems to me that when a discerning adult is interviewing a 13 year old child, it is the rare child who can skillfully hedge the “What other schools are you applying to?” question. By not answering honestly you assume the risk of coming off as not forthright or having something to hide. Besides it may help determine “fit” if you are interested in schools with similar philosophies. I agree that the answer to this question could be used against you, however appearing less than honest may hurt you more.