Isn't that just Wi-Fi Direct? Which I understand establishes a separate, dedicated temporary network for that task over Wi-Fi, with the two devices being the only ones connected to it? Isn't that still two machines on the same network via Wi-Fi, merely separate from prior networks they may have been connected to? How can you claim there is no local network or that the device doesn't need to be on Wi-Fi at all? Surely they need both a local network and Wi-Fi? Or are you referring to Bluetooth-only transfers?

In any case, my point obviously wasn't that I my home router has to see the packets, but whether/when servers on the internet become involved...