Gil has a nice post on the latest mythmaking regarding the Hazon Ish. Along those same lines, there is a farily well known story that goes something like this:
Rabbi Yehoshua Mondshein has collected the various stories and noted the original source in a typically excellent article available here. Also there is a thread on Hyde Park about this article here.
An Orthodox person is sitting in the Jewish National Library and gets hungry. He takes out his lunch and then benches however, he does so in an audible tone. In his recitation he says the words שלא נכשל לעולם ועד. The librarian who is not Orthodox comes over to complain about his eating and he loud blessing. Additionally, she points out the he does not even know how to properly bless in that he used a version that doesn't appear in the blessing, namely, שלא נכשל. He is preturbed by her assertion and claims that is his custom. She then proceeds to pull out all the siddurim to show him that none have it. He goes home and comes across a siddur which does have his version and photocopies it and sends it to her. He circles in red the relevant passage - שלא נכשל.Anyways this is the basic gist of the story. The story appears in a bunch of different places and in slightly differing versions. At times the "man" is identified and at times not. For instance, Ruchuma Shain in her book Reaching the Stars has this story as does the book "The Kiruv Files," Rabbi Sholom Schwadron also has a version of this story. Here is another take on it. In all these instances this story is passed off as true. However, in truth, this is actually a much earlier story written by Shai Agnon. It was published in 1937 in a slightly different format. You can read the original here.
A few years later he recieves an invitation to attend a wedding of someone he does not know. However, he decides to go anyways. Upon getting there the woman - who is the librarian - tells him that now she is marrying an Orthodox person. However, this was not always the case. In fact, she was schedualed to marry a non-Jew (in some stories an Arab). His letter with the circled words שלא נכשל reached her right before the wedding and she took it as a sign. She became Orthodox and now is marrying an Orthodox man.
Rabbi Yehoshua Mondshein has collected the various stories and noted the original source in a typically excellent article available here. Also there is a thread on Hyde Park about this article here.