Well hold on now. Would it be possible, technically, if for example he lived in a small village with a computer and a landline but without internet, and he had a fax machine, could he not develop a method of connecting the reconfigured fax to a node (which has internet access) through that landline and the node would broadcast to the blockchain? Technically he would be sending Bitcoin payments without internet connection.
That would certainly be possible, although there are probably easier ways of doing it than reprogramming a fax machine.
As I said in my reply which you quoted, the individuals themselves don't necessarily need internet access, but the transaction
must reach the internet somehow. If there is a local node with internet access, then any method of getting your signed transaction to that local node to be broadcast would work. Transmitting over telephone lines via a modem, a reprogrammed fax machine, or something else, is certainly a possibility, as is radio, mesh networks, SMS, going there in person with the transaction on a USB drive, and so on.