This link claims that the Siddur Ha'Arizal compiled by Rabbi Asher Margaliot is the siddur that was used by the Ba'al Shem Tov and his original followers. How accurate is it to say this?
Only on the technical basis that it is according to the nusach of the Ari z'l.
The actual expert sofer of the Ba'al Shem Tov was Rabbi Shabbtai of Rashkov. The siddur which the Ba'al Shem Tov used was written by him. Rabbi Shabbtai was an expert on the nusach of the Ari and all his kavanot. There are still manuscript copies of that siddur in Rabbi Shabbtai's own hand in existence. Printed versions of his siddur with all the kavanot can be purchased today.