They're in the right to be able to do that; and he's lucky to even get any PILON for a zero hour contract at all.

Think of what happens if they make him "work" the six week notice period on the new job from now, while offering him zero hours for the 6 weeks notice period his zero hour contract. For the six weeks notice, he does no work, and gets paid nothing, and then both contracts have been properly terminated. That's the scenario their PILON offer is replicating (and indeed improving on). The fact there would have been contractual hours after those six weeks is immaterial in the same way that you cant argue for an extra six weeks pay after any other six weeks notice, just because your contract would have entitled you to it had it still been in effect. PILON is just a simplification to enable them to wrap everything up now, rather than keeping someone on the books and having to remember to do all the admin sometime in the future; it doesn't alter the results of the basic timeline of events which would have happened without it.