While I do believe that whatever is happening will largely be explained by selective attention and confirmation bias, here is at least one instance of a drone sighting on the final approach path to JFK over a landing airplane: https://www.youtube.com/watch?v=HQiSkTVeN78
Why not? Technically it's possible, and while consumer drones often have altitude (above ground) limits, I wouldn't be surprised if these can be modded out.
So I think that's the most likely explanation – surely the US military would not have their drones fly around in an active final approach path of a major civilian airport...? And if it was a foreign military, I really hope that the US wouldn't be as casual about it.
