To avoid is:
to keep out of the way of
That doesn't necessarily require an action. In fact it almost implies a lack of action - the dictionary talks about keeping out of the way of something, but not getting out of the way of something. This contradicts my own personal usage of "to avoid", so I'm not sure a dictionary is actually the best reference for this. I am hence going to rely on my own personal usage:
- I would be happy to use avoid to mean "getting out of the way of something". This would definitely constitute an action. e.g.:
I avoided being hit by the car by jumping inside a shop doorway.
- I would be happy to use avoid to mean "keeping out of the way of something" provided that the "keeping" is deliberate. e.g.:
I normally see Angela on my walk home. Yesterday I didn't want to see anyone I know as I was having a bad hair day, so I avoided Angela by walking a different route.
- I would not be happy to use avoid to mean "keeping out of the way of something accidentally". e.g.:
Incorrect: I normally see Angela on my walk home. Yesterday I didn't see her, maybe I avoided her because she took a different route or walked at a different time.
Correct: I normally see Angela on my walk home. Yesterday I didn't see her, maybe I missed her because she took a different route or walked at a different time.
"Narrowly" is an adverb modifying avoid, it makes no difference to whether to avoid requires a conscious act or not.
In summary: if the skier was oblivious, and made no manoeuvres which took him out of the path of the drone, I do not believe he narrowly avoided being hit by the drone, but I do believe he narrowly missed being hit by the drone.
