We don't know of any technical reason why a fax, or a phone, or any single-line telecom device that normally requires two conductors, would not work just fine with a four-conductor cord, when the extra wires are not connected to anything; but H-P keeps insisting on it.
H-P tech support said that "sometimes the extra two conductors (wires) can act as an antenna and pick up interference that hurts faxing."
We don't understand why Panasonic, Brother, Sharp, NEC and other brands don't worry about it.
However, if your faxing is going gaflooey, (or kaflooey, or kerflooey) and you’re using a four-conductor line cord, there is a chance that the cord is the source of the trouble. So, if you’ve tried everything else, now try the cord that HP recommends. We have 'em. CLICK