and plutonium is much, much harder to set off than HEU. For that reason, accidentally setting off the chemical explosives in a disassembly accident wouldn't have detonated the first plutonium bomb ever built (Gadget/Trinity/"Fat Man"), although the Hiroshima bomb and other gun-type HEU systems would definitely be susceptible to that. For a plutonium implosion system, the explosive lenses have to be detonated within microseconds of each other in order to get a
perfectly symmetrical implosion, and nothing but a synchronized electronic firing impulse will do that. You also need a neutron pulse at just the right time, and I'm thinking the W56 would have used pulse neutron tubes for that purpose, which again have to be electrically fired (it's a little particle accelerator, so it doesn't just "go off").
No, the W56 doesn't have the anti-tampering systems and such that modern warheads have--so an unauthorized
commanded detonation would probably be more feasible (don't let anybody steal it!)--and an accidental core disassembly might be messier with the W56 than with newer designs--but it
is a multistage thermonuclear weapon using a plutonium-based primary, and as such I think sigificant yield from anything other than a commanded detonation is extremely farfetched on physics grounds.
Cary Sublette's Nuclear Weapons FAQ is a FANTASTIC resource for those wishing to understand the technology on a qualitative level. Of course, he leaves out classified details about primary configuration and engineering bits, but it's an excellent overview of the physics. Here are some sections related to the incident described in the OP:
http://nuclearweaponarchive.org/Nwfaq/Nfaq4-1.html#Nfaq4.1http://nuclearweaponarchive.org/Nwfaq/Nfaq4-1.html#Nfaq4.1.6http://nuclearweaponarchive.org/Nwfaq/Nfaq3.html (background on the physics)
Also keep in mind that "core assembly resulting in nuclear yield" is not the same as a full yield explosion, though a reporter could easily get them confused. I'm not saying that accidentally setting off the chemical explosives might not result in a few pounds of nuclear yield in addition to the chemical explosion, just that I don't see any possible way to set off a large-order nuclear detonation in that manner.