I recently came across a story about the Vilna Ga’on in Halachic Man (on p.30 in the 1984 English edition). I had various doubts about the authenticity of the story, and in the course of discussing my doubts with several people I kept hearing the assurance that the Briskers, or the Soloveitchiks, are very careful about such things and can be trusted to tell the story only because they have authenticated it.
How did the Briskers or the Soloveitchiks acquire this reputation for this sort of exactingness?