1. Rav Kook was the mesader kiddushin of both Rav Eliashiv and Rav Shlomo Zalman Auerbach (who before he married was a regular at Rav Kook’s public seuda shelisheet and derasha). Rav Eliashiv was, in fact, married to a daughter of Rav Arye Levine, who was a talmid muvchak of Rav Kook.
2. Rav Hutner was Rav Tzvi Yehuda’s brother-in-law. he incorporated many of Rav Kook’s teachings into his own writings.
3. The “Kook shmook” statement, if the CC said it, obviously referred to what the newspaper attributed to Rav Kook (at the time falsifications of Rav Kook’s statements were being circulated in Poland). It is inconceivable that the CC, who not only literally wrote the book on lashon hara and hotzaat shem raand and received a haskama from the Sefat Emmet after the latter unsuccessfully tried to get him to say lh as a test, would have expressed himself thus on the basis of a newspaper report.