And just how was a student pilot to "assume PIC" when it wasn't legal for him to do so?

Using the emergency clause.

I saw the interview and the writups, and really cannot accept at face
value what was said. It just doesn't wash. But another possibility
occurs to me. I don't know how much time the other pilot had, or how
much recent time. But just suppose...

idle wild speculation
The pilot hadn't flown much lately, was very rusty, and knew it, and
wanted to get to wherever. He's not really fit to do it himself, so
asks the student to fly him. The student was interested in some CC
experience, but of course can't be PIC and can't take passengers. No
problem - the pilot can =be= PIC for the trip, and let the student do
the flying and navigating and such. (Aside from the possibly
inadvertent lack of currency of the pilot) this makes it legal.

They go off, each figuring the other is responsible for this or that
aspect of the flight. The pilot did most of his flying in the old days,
perhaps even before TCAs, but doesn't give the ADIZ depicted on the
chart its due (flying in a TCA area one just ducks under the tiers and
doesn't have to talk to anyone, no big deal, this other thing is
probably the same). The student hasn't gotten to this part of the
curriculum, and accepts the straight line that the pilot has drawn.
They end up where they are, befuddled, each for different reasons.
/idle wild speculation.

Jose
--
The price of freedom is... well... freedom.
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