They aren't giant squids (Architeuthis dux). They are Humboldt squids(Dosidicus gigas), different species and popularly targeted for fishing in (I believe pacific side) Mexico.

The nomenclature mishap is probably due to the other common name for Dosidicus gigas: JUMBO squid. Not "giant". Interestingly, these guys are also known down in Mexico as Diablo Rojo, or the Red Devil. While fishing schools of these guys, they get pretty nasty with all the squid blood in the water, and have been known to attack people stupid enough to try to swim with them. There are also rumors of fishermen falling overboard and being attacked. There was one guy who built a "squid suit" a-la those "bear suits" that have been built, to keep himself safe from a squid attack. He was attacked and pulled down deep enough so violently that he could not equalize pressure in his nose/ear/throat and his eardrum burst.

YouTube - Giant Squid Fishing in San Diego Daylight

YouTube - Humboldt Squid Fishing in San Diego Daylight - Part 2

I'll look for vids of the guy who got attacked by the squid.