This is interesting! As a writer, I usually rely on diagesis a lot - the "movie in my head". So for me, third person limited is the natural choice: it's the camera following the main character around (where first person would be the camera-as-protagonist). That is, you can ask that exact same question of most movies and TV that do not employ the "Blair Witch" in-story footage mode: what viewpoint are we in, and isn't it a completely artificial one in the context of the movie's own universe, considering that there isn't a character standing there whose eyes we're seeing through? (Ans: yes.)

That being said, I think of the narrator as being there in nearly all my stories these days, and also that the narrator is me, or close enough. I don't know to what extent other readers feel this, but no matter how nominally limited the third person, I'm using my turns of phrase and my vocabulary, not the character's. The gap can be minimal, or make for a certain ironic distance. Possibly it's only third limited because there's not that much call to switch perspectives in a short story (my WIP novel is definitely omniscient), but I've always also felt that the "look at me! I know the beginning and end of the tale I will tell you and have a bird's eye view of everything!!" school of omniscient narration to be... gimmicky. Unless that's what one's going for.