The short answer is: often, yes. Nikolai Novikov believes that the Russian peasants used to see the folktales they listened to as fact, but the shift of seeing them as fiction happened towards the end of the nineteenth century. Dmitrii Zelenin "reports that tellers could not always make a clear distinction between truth and invention in the folktale, but most often believed in what they narrated." Zelenin says that belief in Baba Yaga was widespread, and tales about her often incorporated other historical figures such as Orthodox saints (although Johns later states that scholars debate over whether or not Baba Yaga was believed in by the Russian people).
Baba Yaga by Des Hanley
A storyteller's beliefs about the truth of their tales may be found at the conclusion of their story. A Frog Princess tale told by V. P. Monachkova in 1979 took place, she says, "during the reign of Nikolai Nikolaevich." Storyteller Agaf''ia L. Zaitseva believed that the events in the stories could have happened "in the old days," for "Why would the old people lie to us? What would they have to gain by it? There were dragons, knights, and sorceres. And I've seen witches myself."
Some of the evidence gathered about storytelling indicate that people believed that fairy tales themselves were a form of magic. Certain rules applied to what time of the day or the year tales could be told, because it was believed that the tales might produce affects varying from attracting spirits, to causing cows to get lost in the forest forever.
Ivan Bilibin, illustration for Afanasyev's "Father Frost"
Yet of course, to every rule their are exceptions. Other tales end with phrases that indicated that the teller and listener both know very well they are not true, historical facts, such as "That's the whole tale, and I can't lie any more," or "Well, I think this is all chatter. All of this really couldn't happen like that."
Fairy tales have a complex history, and you may come across people making contradictory statements; some claiming that historically, people used to believe the tales they told, and others maintaining that even hundreds of years ago people weren't gullible enough to believe all the details of a story. So both claims are true, and of course it varies from culture to culture. The reality is, many historical facts or legends probably evolved and became more fantastic and grew into fairy tales; other tales were pure invention on the part of the storyteller, embellishing on other tales and story motifs.
Mid-20th Century Cigarette Case from The Russian Museum
Johns points out that folklore itself has almost contradictory aspects of its nature-the stories are set in another, enchanted realm, distinct from the everyday; yet the stories are such that, when you strip the story of its magical and fantastic elements, at its core is a story of human conflict and struggle that we can all relate to. Fairy tales are at once realistic and unrealistic; they have truth in them whether or not that are seen as fiction. Linda Degh says that fairy tale narration is an ambiguous art, for "the teller uses all his or her artistry to make the listeners believe what they know is an entertaining lie." Even today when fairy tales are told, their long history and the level of awe we tend to have towards them makes even the most skeptical of us sometimes wonder about these tales that have captured human imagination for so very long...