Many of our Gedolei Yisroel were in a different world when it came to Bitachon. I was told by a close Talmid of R’ Ahron Kotler Zatzal that he was “treading very lightly on Tevah”, and he did a minimum of Hishtadlus, like knocking on a door “only a drop” when collecting for a Mosad. One knock; I'm “Yotzei” already, and I'm leaving.
I know a story about R’ Ahron Zatzal where he blasted a wealthy person since he didn’t approve of his Treife Shitos, and he really let him have it full force. This is despite that this person was in the process of giving Lakewood a tremendous amount of desperately needed money.
After this episode, R’ Ahron was Mya'esh on getting the money, but he didn’t care. In the end, this person respected R' Ahron and gave him the money nonetheless. I once heard a story about R' Ahron where he was asked by a Torah builder if he can say certain Shitos that weren't 100% kosher, in order to “buy-off” the American “Oilam” who weren't really ready for the “extremism” of Lakewood Shitos. R' Ahron said that with Sheker, you can’t build Emes.
There is a famous story where somebody got up at a parlor meeting and said that Lakewood Yeshiva was there to produce Roshei Yeshivos, Rabbonim, and M’chanchim, etc. for the public. R' Ahron got up and said that the Yeshiva was there for producing people who did nothing but just learning Torah! Surely this wasn’t a view that a practical minded American understood; but R' Ahron didn’t care. And this is exactly why Lakewood was Zoche to have such phenomenal Hatzlacha, since R' Ahron cared only about Hashem’s opinion, and not what “so and so” thinks, etc.
I know many great Novardokers who chose R' Ahron as their Rebbe after WWII, like R' Kalman Goldberg Zatzal and R' Chaim Zaitchik Zatzal [who was the Baal Tefila in Lakewood in R' Ahron’s days on Yamim Nora'im. R' Ahron’s Bitachon and fearlessness of people, his Middas HaEmes, his uncompromising “extremism” for Yiddishkeit, and love for Torah; are familiar concepts in Novardok.
Also, R' Ahron’s disregard for Gashmiyus. I once heard a story where R' Ahron ate his food in a non-conventional way, but it was done in private. The Gadol HaDor [R' Ahron] didn’t do weird things in public, since his “Kavod HaTorah” is Kodesh Kodashim.