I havent seen the show, but I'm going to say not accurate at all. Chernobyl was indeed an explosion like you say, which was caused by power in the reactor increasing to huge levels.
In the fuel bays, there will be no chain reaction of neutrons, all the heat is just decay heat, caused by beta radiation as the fission products decay. The only possibility that even comes to mind for an explosion of any sort is the Zirconium Steam reaction, where steam interacts with the Zr fuel sheath at temps above 1100 C and produces hydrogen, which would pose explosion hazard. Seems really unlikely, but I really don't know.
edit: after saying that, try googling Andreyeva Bay. Apparently the rooskies have some neglected spent fuel, and are at risk of thier fuel breaking down due to salt water, and suspending the fuel in such a way that criticality is reached. That would lead to risk of explosion if conditions were just right.
re-edit: upon furthur review, this whole criticallity in the fuel bay thing seems to be only promoted by a greenpeaceish type group, and therefor is almost guaranteed to be b-s.
Oh my god, Im scared. OK, maybe not.
I'm used to thinking about natural uranium, where you can not arrange the fuel bundles or the fuel pellets in any way to make critical, without moderator.