I don't think the we are 'supposed' to find him unreliable. I don't know that he isn't though. By unreliable, I take to mean that Kvothe's account is somehow questionable. There are a couple instances where Bast shows some surprise or confusion about the story as told. I assume that we are somehow not getting all of the story. Or, if nothing else, just a very specific view of how the tale unfolded. Most people have a somewhat limited perspective of their own stories after all.

Besides, a real storyteller makes a story believable, not always bigger.

I think this is part of Kvothe's motivation, and in part the intended structure for the narrative. We don't get the repeated "Real life isn't like a story" line for nothing. But, that being said, I still get the feeling that something more, or less, is going on at times. There are just a few moments in the narrative that give me pause. (I'll have to page through a few things when i get home to my book... I'll try to be more specific)