xkcd again, but now on linguists and their weird habits
I feel slightly offended. Because it's true.
(Alt text: "Do you feel like the answer depends on whether you're currently in the hole, versus when you refer to the events later after you get out? Assuming you get out.")
I would have guessed that into and in are interchangeable for this case, at least in US English.
But in other contexts into is a direction, in is a position.
Falling into it includes the travel time (potentially from a great height), whereas in mostly pertains to the end state?
That would mean into and down refer to different parts of the falling timeline.
Instead of the travel time, I think that the matter here is the movement: "into" implies movement, so it can be only used when there's a change in position. And the interchangeability in this case is caused by the fact that, while "in" doesn't imply movement, it doesn't imply its lack either.
Other IE languages also show this sort of grammatical movement marking, although through different ways. For reference, in Latin:
cecidi in foveam - I fell into a hole (accusative because movement)
cecidi in foveā - I fell in a hole (dative; I'd interpret it as lack of movement, unlike English "in", but I'm not certain on that)
English also used to have this distinction in the auxiliary verbs that you'd use with the past - "be" if there's movement (even metaphorical), "have" otherwise. You see this for example in Oppenheimer's translation of Bhagavad Gita, "I am become Death" (modern: "I have become Death"), but eventually this usage of "be" was completely replaced with "have". German still does it but... it's complicated since movement itself isn't the sole factor, the main verb also dictates the auxiliary to some degree:
ich bin in ein Loch gefallen - I have fell into a hole
ich *habe in ein Loch gefallen - this simply sounds weird
As a native speaker, that makes sense, but they still both sound interchangeable.
Edit: In this situation, anyway. Other people are pointing out that "down a hole" wouldn't work if it was a hole you couldn't actually be "inside of", like a pothole in a road. In that case "in a hole" would still be okay, as it's a partial kind of "in" like water in a dish.
The pragmatics of the sentence in the comic is that the person is in/down the hole, and this is not a normal state of affairs. The exact sort of envelopment isn't emphasised, and I imagine the choice would come down to exact idiolect. I'd say "down", I picture someone from another province or old for "in".
"Down" definitely implies vertical entry, although it could be an abstract downwards, like "he's further down the tunnel" - an entry is imagined as being at the top by default.