Wouldn't it already be obvious that all dead people come back as zombies (if it is indeed true on this show)? That's a rather hard thing not to figure out by this point in the apocalypse, though they get a little bit of slack given that it takes between two and eight hours to turn...
I'm not sure I buy the timing of all this, though. It might make sense that some of the research locations would run out of fuel, but aren't a lot of military bases designed to run for years post-nuclear explosion? It really hasn't been that long post-apocalypse. Is it possible that the really-secret locations kept their mouths shut in order to keep safe?
A tiny Nuclear reactor in the basement would let that place run for YEARS if not a Decade or two. All you would need is one the size of one that is used in a nuclear sub and access to an underground water source like a well and that facility would be set.