No, I don't think he's very trustworthy because throughout the story you can tell how out of it and demented he is.
Explanation:
I think he just told the story as he lived it, but it might not be what had happened. From the very beginning of the story, he tries to make a case for his sanity, but the story he tells completely undermines it and is at odds with his declarations of sanity. Throughout the story, he recalls the events that led him to murder the old man and then confess. According to the text it states, "'Villains!' I shrieked, 'dissemble no more! I admit the deed!— tear up the planks!—here, here!—it is the beating of his hideous heart!'"
