I think that stories like the ones above should be classified into different categories (Learning, davening, middow, mofsim, etc.) when they are told over. Personally, I like stories that show extraordinary character, and I like the ones that you’d hope to see from every adult less inspiring. I also don’t believe the mofsim.
Two stories (one of which is posted somewhat differently above):
R’ Moshe was hounded by someone who disagreed with something that R’ Moshe had paskened. The man went out of his way to pursue his cause against R’ Moshe. A few months after the issue subsided, another posek (I think the book said R’ Tuvia Goldstein) came to visit R’ Moshe and he saw that antagonist leaving the house. He asked R’ Moshe if the man had come to apologize, and R’ Moshe indicated that the man had not. It turned out that the man had come to ask R’ Moshe for a letter of recommendation because he was trying to find a job. R’ Moshe had written the letter. R’ Tuvia(?) expressed surprise at the man’s chutzpah, and at R’ Moshe’s acquiescence. R’ Moshe said, “The gemara says, “yeish koneh olamo b’sha’ah achas. Maybe this is to be my sha’ah achas.”
(Story was in a book by Rabbi Frand An Offer You Can’t Refuse.)
The other story is about the Satmar Rebbe z’l (R’ Yoel). A collector came to him with a terrible sob story. His wife was sick, and couldn’t deal with their special needs child. His other children were suffering as a result, and the state was threatening to place them in foster care. He himself had gone through painful medical treatments. He was desperate for help so that he could keep his family together and allow his wife to recover.
The Rebbe gave him substantially more than was his custom, and the man left. Shortly thereafter, a chosid came in proclaiming that the man was a fraud. The chosid was disappointed when he saw that he hadn’t managed to warn the Rebbe in time, but when the Rebbe heard the man was a fraud, he said, “So he didn’t have all those tzaros? Baruch Hashem!” (Specific facts were embellished.)