I read Fasetto as Falsetto and figured they were using high-frequency audio to transmit data between phones. An app using that shouldn't have any issue getting approved (just needs speaker/mic), but I suppose the data rate would be pretty low.

It seems that it just tries whatever the device offers. From the kickstarter:

"If Bluetooth isn’t available it can use near field, if near field isn’t available it can use WiFi Direct, if WiFi Direct isn’t available it can use hotspot, and if that isn’t available it can use root sockets (TCP, UDP or any other supported protocol, using any port)."

I'm not sure what "root sockets" means, or how UDP is going to allow you to transmit without WiFi, NFC, or Bluetoth.