The narration of "Dr. Heidegger's Experiment" is a tricky business. We don't really know who the guy is telling the story, and we might not care if he (she?) didn't go to such length to make sure that we worry about it. The narrator continually calls attention to himself and, most importantly, the questionable accuracy of his narrative. Check it out:
Now Dr. Heidegger was a very strange old gentleman, whose eccentricity had become the nucleus for a thousand fantastic stories. Some of these fables, to my shame be it spoken, might possibly be traced back to my own veracious self; and if any passages of the present tale should startle the reader's faith, I must be content to bear the stigma of a fiction monger. (6)
This is an odd and somewhat confusing paragraph. The narrator suggests that he is the source of many stories about Dr. Heidegger – but are these stories true or not? He uses the word "veracious," which basically means "truth-telling." It's possible that this is used ironically; the narrator admits that he has made-up these tales and then calls himself "veracious" with a touch of sarcasm. On the other hand, he might be asserting that these tales are true, but with little or no faith that we'll believe him. He's reconciled himself to this, as we see in the final line.
The bottom line is that we can't know whether or not the narrator is telling us the truth, which is a prime example of the form of the narrative complementing the content of the narrative. Consider the central question that plagues us when it comes to the plot: is the elixir real, or is it a sham? We have to ask the same thing of the narrative itself. Is it real? Is it fantastical? Is it fiction? Is the narrator having a good laugh at our expense, as Dr. Heidegger might be doing to his guests?
You also want to remember that "Dr. Heidegger's Experiment" is highly allegorical. In other words, Hawthorne has a point, and he's not too concerned with subtlety when it comes to getting it across. (See "Genre" for more on this.) Because it is an allegory, it's fitting that the narrative is somewhat divorced from reality. We read it as a set of symbols, caricatures, and exaggerations – not as a realistic tale.