"True" and "truthful" are both adjective and share the same root, and sometimes they mean about the same thing. Therefore I wonder if both of them fit in the above context. If not, why not? Thanks.
Granny Peach is a true story- correct
true = real, conforming to reality ,
Thus, Granny Peach is a real story = They say / It is said that this [Granny Peach] is a real story - I myself don`t know if it`s true
truthful - telling the truth, conforming to truth
a truthful person = a person who tells the truth ; a person you can trust or believe as being true.
e.g. You can trust Jim. He is a truthful person.
If I say that Granny Peach or this story is telling the truth, can you believe it? Are you sure that it can be truthful?
I would say that the difference between true and truthful is ,in fact, the difference, between real and reliable.
we can say that a story is true, not truthful. A story is , in fact, a story.
When it comes to use truthful, you can use it in other contexts :
a truthful person = a reliable person; a person who is telling the truth.= you can rely on her/him because s/he tells the truth.
a truthful statement = a statement conforming to truth
Finally, I`d say that this story is said to be true but I wouldn`t rely on this because I have certain [ to a less or greater degree] doubts about it.