Botany Bay must have had some sort of supplies onboard. Even Khan would need materials to build a home on a new planet. He just got supplemented by the Enterprise. Cargo carriers instead of tents, etc.
I'd imagine that only Starfleet personnel went back aboard the Botany Bay and everything was throughly checked before it was sent down to Ceti Alpha V. The rest of the ship was probably towed to a Starfleet facility and the historians went over it with a fine toothed comb. It's probably in a museum now that Khan and his followers are dead.