He’s wrong at 13:50 and the high frequencies goes though the upper wire and the low frequencies go through the lower wire.
When he says the "signal" he is referring to the "potential" to take the signal from there, but as he shows, only the current for each driver travels through it’s respective wire. If only the current for that driver is traveling through the wire, then only that portion of the signal is traveling through the wire that point in time.
But at 17:16, he shows that the full signal is still in each wire. WRONG. He is only showing that the potential to take the signal from that place is full range. HE NEVER PUTS THE SCOPE IN SERIES WITH EACH WIRE TO SHOW WHAT IS ACTUALLY GOING THROUGH IT! Sure the potential is there at the terminals, but unless you use that potential, it is not manifested.
Another flaw is that he brings the wires back together before they reach the amp giving them a "bridge" before they can "dump" into the amp’s ground. For best results, he should be using the amp’s terminals.
Then when he actually examines what is going down each wire, like he did for the current used, rather that what is just "available" from the pair, I’ll reconsider.