For a melt-down or partial meltdown it is not needed that radioactivity leaks to the outside. That is not how most reactors work. From my understanding a reactor could be in the situation of a complete meltdown without much radiocitivity leaking to the outside (see Three Miles Island). One of the bigest risks are the outer shell not whistanding the heat or possible explosions from waporated water (detonating gas). The contamination of groundwater was some risk which was present in Chernobyle even after the explosion when the reactor was still burning and why they even tried to dig up a tunnel under the reactor to instal a cooling system.