From her description and my own experience, I'm pretty sure the worms are juvenile tapeworms. I've often seen them in beached squid, still energetically crawling around long after the squid has died, and it's always a bit sad.
See, we tend to think of tapeworms (if we think of them at all beyond EW!) as creatures that are as long as an intestine, and constantly breaking off little reproductive bits of themselves to be dispersed with their host's solid waste. But that's just grown-up tapeworms. Juvenile tapeworms are considerably shorter and stay in one piece, and they generally parasitize different animals. Adults live in definitive hosts; juveniles in intermediate hosts.
Tetraphyllid tapeworms like the ones in Humboldt squid actually have two intermediate hosts. Larvae parasitize little planktonic copepods, juveniles live in medium-size marine beasties (fish, shrimp, squid), and adults settle down in sharks or rays. Transmission occurs by consumption; in other words, a copepod is eaten by a squid is eaten by a shark, and the tapeworm goes along for the ride.
But if the food chain is broken, the tapeworm is out of luck. Squid that end up on the beach instead of being chomped by a shark are stranding not only themselves, but their unlucky tapeworm passengers.