I used AirDrop on an airplane at cruising altitude over the ocean, with no onboard wifi available. It worked just as perfectly as it did at home.
The pilot had taken a video of the Falcon 9 second stage separating from the first on its first launch that docked with the ISS. He then walked through the cabin sharing with anyone that was interested.
That is correct, AirDrop works without Internet. It's unfortunate that Google and Apple have created these respective systems with no cross-compatibility. There's really no technological reason for it, but an obvious business reason.
And if it was purely peer-to-peer people would complain that it doesn't work in their particular use case. Personally, it's rather nice sometimes to 'fire and forget' a file transfer with a tool like this. All I need to worry about is if I successfully uploaded the file. I don't need to worry about their internet connection, keeping some daemon running on my side, keeping power on my side, remembering to delete that file that I only kept around so somebody could download it from my computer, etc.
The point is, options are good. Most of us subscribe to the Unix philosophy of "Write programs that do one thing and do it well" so why are so many advocating for a pancea solution that does everything for every use case?
If you're somewhere with poor (or no) network connectivity you can still use Google Files or AirDrop (I believe, not 100% sure on AirDrop).