People often claim that charedi gedolim books make up stories that are just not accurate. Or, they embellish true stories to make them "better". This is true. Some stories really did not happen as told.
Recently, an academic scholar wrote a biography of the saintly Chazon Ish ztz"l. According to a scathing book review, on line here, the book is riddled with inaccuracies. So from here we learn, that the seemingly objective world of academia has no monopoly on truth.
In general, when you hear a story, it is worthwhile taking it with a grain of salt unless you verified the source as accurate. They are enough true woundrous stories about tzaddikim that we don't have to make up any new ones.
The Rebbe Shlita is very careful to tell stories that he either witnessed or heard firsthand from a reliable source. I have learned much from this practice.