When I was in Israel, I found out that some religious zionists have a very confused notion about these rabbis.
Background info: We all know that Rav Avraham Yitzhak HaKohen Kook zt'l was the chief rabbi, posek hador, great religious leader and mystic in Eretz Yisrael until he passed away in 1935. He spearheaded the religious zionist movement and was one of the most profound Jewish thinkers of modern times. His son was his closest student - Rabbi Tzvi Yehuda Kook zt'l and he was a major leader of the settlement movement. He sent out all his top students to build settlements and lead as community rov's there. Some of his top students were: Rabbi Dov Lior (rav of Kiryat Arba/Hevron), Rabbi Druckman, Rabbi Levinger, Rabbi Yakov Ariel, Rabbi Aviner, among others.
The amazing thing is that students of Aviner will insist that only he, Rabbi Druckman, and one other among the major students of Rav T.Y. Kook (I can't remember the third one right now) were actually Rav Tzvi Yehuda's top students and are the only ones who can properly teach or represent his Torah teachings, and in turn, he (Rav Tzvi Yehuda) is the only one who can possibly teach or represent his father's teachings. Thus, only Aviner, Druckman, and one other rabbi who was in favor of obeying orders in gaza expulsion can properly express Rav Kook's teachings and his son's teachings and are authentic leaders of religious zionism or authentic followers of Rav Kook according to these robots. Even though there are other of his top students who even lead communities, they claim that they are not true students of Rav Kook!
And of course any scholar can study Rav Kook's teachings in his published work, there is no monopoly on who presents his views or what they are but that is what these people claim!