R. Chaim Sanzer is a legendary Chasidic figure, father of Hasidism in Galicia, the progenitor of many Chasidim and Chasidic groups, such as Sanz, Bobov, Klausenberg, Zmigrod, Gorlitz, etc.
He said the following related to Chasidic stories - 'When a Chasid says he saw a miracle, he heard it. When he says he heard it, he plainly invented it.'
So states Rabbi Adin Steinsaltz in "My Rebbe", his recent book on the last Lubavitcher Rebbe, on p.173.
There is also an old Chasidic teaching re stories of the Baal Shem Tov, that says 'If someone believes all the stories of the Baal Shem Tov, he is a fool. If he says that they couldn't have happened, then he is an apikoros.'
The above two Chasidic teachings (there are other of the kind as well) are an admission by Chasidim themselves that reliability is an issue with Chasidic stories.
It seems that there are a number of different aspects of this.
Firstly, in general, stories often become transformed as they are passed along by people. That is a general problem of accuracy of transmission, not limited to Chasidic stories. Secondly, with Chasidic stories, there is also a problem of exaggeration, if not fabrication. Some people believe that they are allowed to change the facts for (in their eyes) a good cause. Like 'frumkeit', or 'emunas tzadikim'. Some of these issues re veracity of stories exist for some outside the Chasidic world as well.
The Satmar Rebbe, R. Joel Teitelbaum, who was heavily influenced by Sanz, was known to make fun of Chasidic miracle tales.
I believe other Chasidic leaders came out strongly against falsification of history too.
The main thing is, we must remember what our Torah teaches - מדבר שקר תרחק - one should stay far away from falsehood. There is a Chasidic vort that interprets מדבר שקר תרחק homiletically, that midevar sheker, from falsehood, tirchak, you will distance yourself from Hashem. One cannot sell or build a religion of truth, a Toras Emes, with falsehood. Maybe Hashem help us stay on the path of truth.