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.