The core was officially full of lead. You think they'd admit to anyone, let alone Russia, that a nuke lay on the seafloor? We already know what huge lengths both sides went to to salvage known marine tech wreckage from one another.
Apparently Tybee island was also a dummy device. It later emerged that it was a full on bomb.
Just saying that they had and continue to have every motive to say it's made of lead.