I suspect that by "transferring" the files they mean "transferring a token allowing the recipient to access the files from your plug". From there, under their (debatable) underlying assumption that accessing files from a plug from your device is fast, it's as if the data has been transferred: recipient can view the files on their device, except they're being fetched from your plug (and maybe copied to their own plug in the background).
(Caution, this is just speculation.)